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$The sum to n terms of the series \frac{3}{1^{2}} + \frac{5}{1^{2} + 2^{2}} + \frac{7}{1^{2} + 2^{2} + 3^{2}} + \dots is$

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6nn+1

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Correct option is A

Tn=(2n+1)6n(n+1)(2n+1)=61n−1n+1 ∴Sn=∑Tn=6nn+1

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The sum to n terms of the series 312+512+22+712+22+32+… is

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$The sum to n terms of the series \frac{3}{1^{2}} + \frac{5}{1^{2} + 2^{2}} + \frac{7}{1^{2} + 2^{2} + 3^{2}} + \dots is$