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Summing Consecutive Terms and Pair Determination (Posted on 2015-11-21) Difficulty: 3 of 5
The sequence S1, S2, S3, ..... is defined by:

Sk = 1/(k2 + k), for k=1,2,.....

Find M and N, given that:

SM+ SM+1+ .....+SN = 1/29

No Solution Yet Submitted by K Sengupta    
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Solution Slight variant solution | Comment 2 of 3 |
See the previous post for how the sum of terms simplifies.

I let A=the number of terms so N+1=M+A
so the sum can be written as A/((M(M+A))
setting this to 1/29 gives
A=M^2/(29-M)
and since M is prime the denominator must be 1 so M=28.
A=784
N=811

  Posted by Jer on 2015-11-21 12:48:22
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