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Mikko
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S=1/2+1/6+1/12..............+1/10100, Find S.



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abhishekik
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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.
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shkusira
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Fantastic Abhishek! How did you think of this? i could hardly spot the pattern!

Thanks
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Mikko
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abhishekik
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.
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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
.....
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Economist
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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
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.
Show more
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abhishekik
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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.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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