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Let S1, S2, S3, S4, S5, ....Sn are the s...

Let `S_1, S_2, S_3, S_4, S_5, ....S_n` are the sums of infinite geometric series whose first terms are `1,2,3,4,-5, ... n` and whose common ratios are `1/2, 1/3, 1/4, 1/5, 1/6 ..., 1/n+1` respectively. If `S_1^2+S_3^2+S_5^2+S_7^2+...+S_99^2=100 k`, then find the value of `k`

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The correct Answer is:
1.717
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