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Summing Consecutive Terms and Pair Determination (
Posted on 20151121
)
The sequence S
_{1}
, S
_{2}
, S
_{3}
, ..... is defined by:
S
_{k}
= 1/(k
^{2}
+ k), for k=1,2,.....
Find M and N, given that:
S
_{M}
+ S
_{M+1}
+ .....+S
_{N}
= 1/29
No Solution Yet
Submitted by
K Sengupta
No Rating
Comments: (
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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/(29M)
and since M is prime the denominator must be 1 so M=28.
A=784
N=811
Posted by
Jer
on 20151121 12:48:22
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