jee-main 2023 Q63

jee-main · India · session1_01feb_shift1 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP

The sum to 10 terms of the series $\frac{1}{1 + 1^2 + 1^4} + \frac{2}{1 + 2^2 + 2^4} + \frac{3}{1 + 3^2 + 3^4} + \ldots$ is:
(1) $\frac{59}{111}$
(2) $\frac{55}{111}$
(3) $\frac{56}{111}$
(4) $\frac{58}{111}$

The sum to 10 terms of the series $\frac{1}{1 + 1^2 + 1^4} + \frac{2}{1 + 2^2 + 2^4} + \frac{3}{1 + 3^2 + 3^4} + \ldots$ is:\\
(1) $\frac{59}{111}$\\
(2) $\frac{55}{111}$\\
(3) $\frac{56}{111}$\\
(4) $\frac{58}{111}$

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