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Sum

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Manager
Manager
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Joined: 25 Mar 2009
Posts: 54

Kudos [?]: 19 [0], given: 9

Sum [#permalink]

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New post 08 Apr 2009, 01:19
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S=1/2+1/6+1/12..............+1/10100, Find S.

Kudos [?]: 19 [0], given: 9

Intern
Intern
avatar
Joined: 07 Feb 2009
Posts: 48

Kudos [?]: 16 [0], given: 1

Re: Sum [#permalink]

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New post 08 Apr 2009, 05:20
Nice question Mikko,

I enjoyed solving this.

My answer is 100/101.

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.

Kudos [?]: 16 [0], given: 1

Manager
Manager
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Joined: 02 Mar 2009
Posts: 134

Kudos [?]: 52 [0], given: 0

Re: Sum [#permalink]

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

Thanks

Kudos [?]: 52 [0], given: 0

Manager
Manager
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Joined: 25 Mar 2009
Posts: 54

Kudos [?]: 19 [0], given: 9

Re: Sum [#permalink]

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

I enjoyed solving this.

My answer is 100/101.

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
.....

Kudos [?]: 19 [0], given: 9

Director
Director
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Joined: 01 Apr 2008
Posts: 879

Kudos [?]: 815 [0], given: 18

Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Sum [#permalink]

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New post 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.

My answer is 100/101.

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.

Kudos [?]: 815 [0], given: 18

Intern
Intern
avatar
Joined: 07 Feb 2009
Posts: 48

Kudos [?]: 16 [0], given: 1

Re: Sum [#permalink]

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New post 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.

Kudos [?]: 16 [0], given: 1

Re: Sum   [#permalink] 10 Apr 2009, 05:55
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