jee-main 2021 Q61

jee-main · India · session4_31aug_shift1 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP

The sum of 10 terms of the series $\frac { 3 } { 1 ^ { 2 } \times 2 ^ { 2 } } + \frac { 5 } { 2 ^ { 2 } \times 3 ^ { 2 } } + \frac { 7 } { 3 ^ { 2 } \times 4 ^ { 2 } } + \ldots$ is :
(1) $\frac { 143 } { 144 }$
(2) $\frac { 99 } { 100 }$
(3) 1
(4) $\frac { 120 } { 121 }$

The sum of 10 terms of the series $\frac { 3 } { 1 ^ { 2 } \times 2 ^ { 2 } } + \frac { 5 } { 2 ^ { 2 } \times 3 ^ { 2 } } + \frac { 7 } { 3 ^ { 2 } \times 4 ^ { 2 } } + \ldots$ is :\\
(1) $\frac { 143 } { 144 }$\\
(2) $\frac { 99 } { 100 }$\\
(3) 1\\
(4) $\frac { 120 } { 121 }$

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