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Let $s_{n} = \sum_{k = 1}^{n} \frac{2 k^{2} + 4 k + 1}{{(k^{2} + k)}^{2}}$
COLUMN - I
COLUMN – II
1
$I f s_{10} = λ, t h e n, [λ] =$
Where [.] denotes G I F
P 1
2
$I f s_{9} = μ, t h e n, [μ] =$
Where [.] denotes G I F
Q 2
3
$I f s_{\infty} = m, t h e n, [m] =$
Where [.] denotes G I F
R 4
4
$I f s_{8} = α, t h e n, [α] =$
Where [.] denotes G I F
S 3

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1 - Q, 2 - S, 3 - P, 4 - R

1 - Q, 2 - Q, 3 - S, 4 - Q

1 - S, 2 - Q, 3 - R, 4 - Q

1 - Q, 2 - Q, 3 - Q, 4 - S

answer is B.

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Detailed Solution

$s_{n} = \sum_{k = 1}^{n} \frac{2 k^{2} + 4 k + 1}{{(k^{2} + k)}^{2}} = 2 (\frac{1}{n} - \frac{1}{n + 1}) + (\frac{1}{n^{2}} - \frac{1}{{(n + 1)}^{2}})$

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