Sequence and Series: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jun, Evening shift · Q45

JEE Main 202228 Jun, Evening shiftMathematicsMediumSequence and Series179× since 2002

Let for n = 1, 2, ......, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is

{1 \over {{{(n + 1)}^2}}}

. Then the value of

{1 \over {26}} + \sum\limits_{n = 1}^{50} {\left( {{S_n} + {2 \over {n + 1}} - n - 1} \right)}

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 · 28 Jun, Evening shift · Q45

JEE Main 202228 Jun, Evening shiftMathematicsMediumSequence and Series179× since 2002

Let for n = 1, 2, ......, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is

{1 \over {{{(n + 1)}^2}}}

. Then the value of

{1 \over {26}} + \sum\limits_{n = 1}^{50} {\left( {{S_n} + {2 \over {n + 1}} - n - 1} \right)}

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.

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