jee-main 2023 Q65

jee-main · India · session2_12apr_shift1 Sequences and series, recurrence and convergence Summation of sequence terms

Let $\left\langle a _ { n } \right\rangle$ be a sequence such that $a _ { 1 } + a _ { 2 } + \ldots + a _ { n } = \frac { n ^ { 2 } + 3 n } { ( n + 1 ) ( n + 2 ) }$. If $28 \sum _ { k = 1 } ^ { 10 } \frac { 1 } { a _ { k } } = p _ { 1 } p _ { 2 } p _ { 3 } \ldots p _ { m }$, where $p _ { 1 } , p _ { 2 } , \ldots p _ { m }$ are the first $m$ prime numbers, then $m$ is equal to
(1) 5
(2) 8
(3) 6
(4) 7

Let $\left\langle a _ { n } \right\rangle$ be a sequence such that $a _ { 1 } + a _ { 2 } + \ldots + a _ { n } = \frac { n ^ { 2 } + 3 n } { ( n + 1 ) ( n + 2 ) }$. If $28 \sum _ { k = 1 } ^ { 10 } \frac { 1 } { a _ { k } } = p _ { 1 } p _ { 2 } p _ { 3 } \ldots p _ { m }$, where $p _ { 1 } , p _ { 2 } , \ldots p _ { m }$ are the first $m$ prime numbers, then $m$ is equal to\\
(1) 5\\
(2) 8\\
(3) 6\\
(4) 7

Paper Questions

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