perplexus.info :: Sequences : Summing Consecutive Terms and Pair Determination

Summing Consecutive Terms and Pair Determination (Posted on 2015-11-21)

The sequence S₁, S₂, S₃, ..... is defined by:

S_k = 1/(k² + k), for k=1,2,.....

Find M and N, given that:

S_M+ S_M+1+ .....+S_N = 1/29

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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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