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What is 1/(1)*(2) + 1/(2)*(3) + 1/(3)*(4) + /1(4)*(5) +....

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Re: What is 1/(1)*(2) + 1/(2)*(3) + 1/(3)*(4) + /1(4)*(5) +....  [#permalink]

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New post 03 Aug 2015, 14:01
RIght off the bat, you can see that 1/2 + 1/4 = 3/4. So, the answer is already greater that choices A), B) or C). Based on the acscending nature of the answer choices, we can conclude that 46/55 is less than 9/10. But just using some reasoning, we are already at .75, 1/90 is a bit more than .01, 1/30 is a bit more than .03, 1/20 is .05. Adding these into .75, we are already at .84. Knowing the other 3 terms will give us approximately another .05, we can safely choose answer choice E.
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Re: What is 1/(1)*(2) + 1/(2)*(3) + 1/(3)*(4) + /1(4)*(5) +....  [#permalink]

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New post 20 Dec 2016, 05:10
Hi, solved it in 1 min 32 sec.
Pattern: n/n+1 ==> 9/9+1 Answer E
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What is 1/(1)*(2) + 1/(2)*(3) + 1/(3)*(4) + /1(4)*(5) +....  [#permalink]

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New post 20 Dec 2016, 07:14
goodyear2013 wrote:
What is 1/(1)*(2) + 1/(2)*(3) + 1/(3)*(4) + /1(4)*(5) + /1(5)*(6) + 1/(6)*(7) + 1/(7)*(8) + 1/(8)*(9) + 1/(9)*(10)?

2/5
3/5
7/10
46/55
9/10

Hi,
I want to know what is the best way to solve this question in 2min, please.


Hi Experts, Please correct if my approach is wrong.

1/2 + 1/6 +1/12 = .5 + .16 + .08 = .74 > 7/10, So choices A, B & C are out. Now, as 1/90 is multiple of 10, denominator will also be a multiple of 10 and hence choice D is also out.

Thus, Answer is choice E

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Re: What is 1/(1)*(2) + 1/(2)*(3) + 1/(3)*(4) + /1(4)*(5) +....  [#permalink]

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New post 03 Dec 2017, 06:59
This is from the NCERT text book of math for class 11 in indian school.



PareshGmat wrote:
GyanOne wrote:
Tn = nth term of the series = 1/(n)(n+1) = (n+1-n)/(n)(n+1) = 1/n - 1/(n+1)

If you add all the terms of this series (to n terms), you get a sum of 1 - 1/(n+1) as all the other terms cancel out.
So sum of 9 terms = 1 - 1/10 = 9/10.
Option (E).


This is excellent. How long it took to derive the formula?

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Re: What is 1/(1)*(2) + 1/(2)*(3) + 1/(3)*(4) + /1(4)*(5) +.... &nbs [#permalink] 03 Dec 2017, 06:59

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