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Algebra - summing up using Sigma notation

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Algebra - summing up using Sigma notation  [#permalink]

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New post 24 Jan 2018, 06:35
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Hi!
I'd be incredibly greatful if you could provide me with a bit deeper explenation of the excercise below than it's in the Official Guide (pls see in the attachment).

"For any positive inteer n, the sum of the first n positive integers equals [n(n+1)][/2] . What is the sum of all the even integers between 99 and 301?"
a) 10,100
b) 20,200
c) 22,650
d) 40,200
e) 45,150

Why exactly does one have to use the sum of the 150 even integers and the substract the sum of the 49?

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Posts: 48041
Re: Algebra - summing up using Sigma notation  [#permalink]

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New post 24 Jan 2018, 06:40
KarolinaBambi wrote:
Hi!
I'd be incredibly greatful if you could provide me with a bit deeper explenation of the excercise below than it's in the Official Guide (pls see in the attachment).

"For any positive inteer n, the sum of the first n positive integers equals [n(n+1)][/2] . What is the sum of all the even integers between 99 and 301?"
a) 10,100
b) 20,200
c) 22,650
d) 40,200
e) 45,150

Why exactly does one have to use the sum of the 150 even integers and the substract the sum of the 49?


This question is discussed here: https://gmatclub.com/forum/for-any-posi ... 27817.html

In case of any further questions please post there.
_________________

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Math Expert
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Joined: 02 Sep 2009
Posts: 48041
Re: Algebra - summing up using Sigma notation  [#permalink]

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New post 24 Jan 2018, 08:08
KarolinaBambi wrote:
Hi!
I'd be incredibly greatful if you could provide me with a bit deeper explenation of the excercise below than it's in the Official Guide (pls see in the attachment).

"For any positive inteer n, the sum of the first n positive integers equals [n(n+1)][/2] . What is the sum of all the even integers between 99 and 301?"
a) 10,100
b) 20,200
c) 22,650
d) 40,200
e) 45,150

Why exactly does one have to use the sum of the 150 even integers and the substract the sum of the 49?


Please read carefully and follow our RULES OF POSTING. Thank you.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: Algebra - summing up using Sigma notation &nbs [#permalink] 24 Jan 2018, 08:08
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