It is currently 19 Mar 2018, 11:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Sum

Author Message
Manager
Joined: 25 Mar 2009
Posts: 54

### Show Tags

08 Apr 2009, 01:19
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

S=1/2+1/6+1/12..............+1/10100, Find S.
Intern
Joined: 07 Feb 2009
Posts: 47

### Show Tags

08 Apr 2009, 05:20
Nice question Mikko,

I enjoyed solving this.

Explanation:

S=1/2+1/6+1/12..............+1/10100
or, S=(1-1/2)+(1/2-1/3)+(1/3-1/4)+..............+(1/100-1/101),
every term gets canceled except first and last.

so, S=1-1/101
or, S=100/101.
Manager
Joined: 02 Mar 2009
Posts: 130

### Show Tags

08 Apr 2009, 08:38
Fantastic Abhishek! How did you think of this? i could hardly spot the pattern!

Thanks
Manager
Joined: 25 Mar 2009
Posts: 54

### Show Tags

09 Apr 2009, 03:48
abhishekik wrote:
Nice question Mikko,

I enjoyed solving this.

Explanation:

S=1/2+1/6+1/12..............+1/10100
or, S=(1-1/2)+(1/2-1/3)+(1/3-1/4)+..............+(1/100-1/101),
every term gets canceled except first and last.

so, S=1-1/101
or, S=100/101.

Yes, totaly agree with you, a little more detailed:

1/2=1/(1*2)=(2-1)/2*3=1/2-1/3 (it 's more obvious when u put it in fraction )
1/6=1/(2*3)=1/2-1/3
.....
Director
Joined: 01 Apr 2008
Posts: 847
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

### Show Tags

10 Apr 2009, 01:39
Dude how did u think abt this pattern...can you tell the line of thought? I tried to see if it is a AP or GP..but then couldnt think of this pattern...
abhishekik wrote:
Nice question Mikko,

I enjoyed solving this.

Explanation:

S=1/2+1/6+1/12..............+1/10100
or, S=(1-1/2)+(1/2-1/3)+(1/3-1/4)+..............+(1/100-1/101),
every term gets canceled except first and last.

so, S=1-1/101
or, S=100/101.
Intern
Joined: 07 Feb 2009
Posts: 47

### Show Tags

10 Apr 2009, 05:55
10100 helped me to find this pattern.
10100 clearly looked like 101x100, then I came to know that 2 is also 2x1, 6- 3x2, 12- 4x3 etc.
and I just tried the ways to break 1/2 using 2x1, 1/6 using 3x2 and so on. Finally, I got this solution.
Re: Sum   [#permalink] 10 Apr 2009, 05:55
Display posts from previous: Sort by
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}