January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 7198

What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
20 Feb 2018, 06:55
Question Stats:
60% (01:44) correct 40% (01:45) wrong based on 183 sessions
HideShow timer Statistics
What is the value of \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3....+50}\)? (A) \(2\) (B) \(\frac{100}{51}\) (C) \(1\) (D) \(\frac{50}{51}\) (E) \(\frac{49}{50}\) New question... Kudos for best solutions
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82

What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
20 Feb 2018, 08:06
chetan2u wrote: What is the value of \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3....+50}\)? (A) \(\frac{49}{100}\) (B) \(\frac{49}{50}\) (C) \(1\) (D) \(\frac{49}{25}\) (E) \(\frac{49}{10}\)
New question... Kudos for best solutions \(1= 2\frac{2}{2}\) \(\frac{1}{(1+2)}=\frac{2}{2}\frac{2}{3}\) \(\frac{1}{(1+2+3)}=\frac{2}{3}\frac{2}{4}\) and so on, hence last term will be \(\frac{1}{(1+2+3+....50)}=\frac{2}{50}\frac{2}{51}\), on adding all the above numbers we will get \(2\frac{2}{51}=\frac{100}{51}\)  The formula for this type of series is \(\frac{2n}{(n+1)}\), where \(n\) is the number of term., here we have \(50\) terms so the addition should be \(\frac{2*50}{(50+1)}=\frac{100}{51}\)



Director
Joined: 14 Nov 2014
Posts: 632
Location: India
GPA: 3.76

What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
Updated on: 20 Feb 2018, 08:22
chetan2u wrote: What is the value of \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3....+50}\)? (A) \(\frac{49}{100}\) (B) \(\frac{49}{50}\) (C) \(1\) (D) \(\frac{49}{25}\) (E) \(\frac{49}{10}\)
New question... Kudos for best solutions Hi Chetan2uI am getting 100/51 if we will see the denominator : it is sum of consecutive integer : \(\frac{n*(n+1)}{2}\) the expression can be broken down into \(\frac{2}{n*n(n+1)}\)  where n = 1 to 50 further we can write it as\(\frac{2}{n}\)  \(\frac{2}{n+1}\) where n = 1 to 50 now 1st term\(\frac{2}{1}\) \(\frac{2}{2}\)1st \(\frac{2}{2}\)  \(\frac{2}{3}\)2nd .. similarly it will go till \(\frac{2}{50}\)  \(\frac{2}{51}\)50th each fraction wil be cancel out except 2 \(\frac{2}{51}\) =\(\frac{100}{51}\)
Originally posted by sobby on 20 Feb 2018, 08:10.
Last edited by sobby on 20 Feb 2018, 08:22, edited 1 time in total.



Math Expert
Joined: 02 Aug 2009
Posts: 7198

Re: What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
20 Feb 2018, 08:21
niks18 wrote: chetan2u wrote: What is the value of \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3....+50}\)? (A) \(\frac{49}{100}\) (B) \(\frac{49}{50}\) (C) \(1\) (D) \(\frac{49}{25}\) (E) \(\frac{49}{10}\)
New question... Kudos for best solutions \(1= 2\frac{2}{2}\) \(\frac{1}{(1+2)}=\frac{2}{2}\frac{2}{3}\) \(\frac{1}{(1+2+3)}=\frac{2}{3}\frac{2}{4}\) and so on, hence last term will be \(\frac{1}{(1+2+3+....50)}=\frac{2}{50}\frac{2}{51}\), on adding all the above numbers we will get \(2\frac{2}{51}=\frac{100}{51}\) Hi chetan2u, can you clarify what I am missing here. also the formula for this type of series is \(\frac{2n}{(n+1)}\), where n is the number of term., here we have 50 terms so the addition should be \(\frac{2*50}{(50+1)}=\frac{100}{51}\) same as my answer, if there had been only 1 term, then the sum would have been 2*1(1+1)=1, i.e. the first term in the series. Hi.. you are absolutely correct.. Actually in hurry, I added the choices of a similar question I had made Edited .. thanks and kudos
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82

Re: What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
20 Feb 2018, 08:54
chetan2u wrote: niks18 wrote: chetan2u wrote: What is the value of \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3....+50}\)? (A) \(\frac{49}{100}\) (B) \(\frac{49}{50}\) (C) \(1\) (D) \(\frac{49}{25}\) (E) \(\frac{49}{10}\)
New question... Kudos for best solutions \(1= 2\frac{2}{2}\) \(\frac{1}{(1+2)}=\frac{2}{2}\frac{2}{3}\) \(\frac{1}{(1+2+3)}=\frac{2}{3}\frac{2}{4}\) and so on, hence last term will be \(\frac{1}{(1+2+3+....50)}=\frac{2}{50}\frac{2}{51}\), on adding all the above numbers we will get \(2\frac{2}{51}=\frac{100}{51}\) Hi chetan2u, can you clarify what I am missing here. also the formula for this type of series is \(\frac{2n}{(n+1)}\), where n is the number of term., here we have 50 terms so the addition should be \(\frac{2*50}{(50+1)}=\frac{100}{51}\) same as my answer, if there had been only 1 term, then the sum would have been 2*1(1+1)=1, i.e. the first term in the series. Hi.. you are absolutely correct.. Actually in hurry, I added the choices of a similar question I had made Edited .. thanks and kudos Thanks chetan2u for updating. Nonetheless its a great question



Director
Joined: 31 Jul 2017
Posts: 517
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
20 Feb 2018, 09:03
chetan2u wrote: What is the value of \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3....+50}\)? (A) \(2\) (B) \(\frac{100}{51}\) (C) \(1\) (D) \(\frac{50}{51}\) (E) \(\frac{49}{50}\)
New question... Kudos for best solutions We know that \(1+2+…+n\)=\(\frac{n(n+1)}{2}\) Therefore, the nth term is = \(1/\frac{n(n+1)}{2}\) or, nth term = \(2[\frac{1}{n}  \frac{1}{n+1}]\) As you can see, when we add from n = 1 to n = 50, all numbers will cancel out accept  \(2[1  \frac{1}{51}] = \frac{100}{51}\)
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Intern
Joined: 11 Nov 2017
Posts: 3
Location: Kazakhstan
Concentration: Human Resources, Entrepreneurship
GPA: 3.29

Re: What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
01 Mar 2018, 03:15
chetan2u, hello! Thank you for the question! Accidentially I cannot understand the explanation, can you please explain the solution in details? Thank you in advance!



Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82

Re: What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
01 Mar 2018, 08:05
AkbarShakenov wrote: chetan2u, hello! Thank you for the question! Accidentially I cannot understand the explanation, can you please explain the solution in details? Thank you in advance! Hi AkbarShakenovin this type of series question, you need to identify the patterns. Each term in the series will follow a similar pattern. so first term of the series 1 can be written as 22/2 second term 1/(1+2)=1/3 can be written as 2/22/3. Note the relationship between first term and second term 2/2 is common in both the terms but has opposite signs. Hence when we will add all the individual terms, common terms will get cancelled. similarly you can rewrite each term of the original series as a difference of two different numbers. Depending upon the level of question, the pattern can be easy or difficult to identify. In most case the first two terms should be able to provide you a pattern.



Intern
Joined: 11 Nov 2017
Posts: 3
Location: Kazakhstan
Concentration: Human Resources, Entrepreneurship
GPA: 3.29

Re: What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
05 Mar 2018, 02:15



Intern
Joined: 12 Mar 2018
Posts: 2

Re: What is the value of 1+1/(1+2)+1/(1+2+3)
[#permalink]
Show Tags
13 Mar 2018, 17:52
I do not think the propose of this question is about calculation, If we see the equation carefully, it has 1 and other positive fractions in the equation, so we can let C,D,E out, because they are <=1, then we know that all the sums of the fractions can not be superior than 1, so let A out, we have only B to choose.




Re: What is the value of 1+1/(1+2)+1/(1+2+3) &nbs
[#permalink]
13 Mar 2018, 17:52






