jee-advanced 2013 Q45

jee-advanced · India · paper2 Sequences and Series Limit Evaluation Involving Sequences

For $a \in \mathbb { R }$ (the set of all real numbers), $a \neq - 1$, $$\lim _ { \mathrm { n } \rightarrow \infty } \frac { \left( 1 ^ { a } + 2 ^ { a } + \ldots + \mathrm { n } ^ { a } \right) } { ( n + 1 ) ^ { a - 1 } [ ( n a + 1 ) + ( n a + 2 ) + \ldots + ( n a + n ) ] } = \frac { 1 } { 60 }$$ Then $a =$
(A) 5
(B) 7
(C) $\frac { - 15 } { 2 }$
(D) $\frac { - 17 } { 2 }$

For $a \in \mathbb { R }$ (the set of all real numbers), $a \neq - 1$,
$$\lim _ { \mathrm { n } \rightarrow \infty } \frac { \left( 1 ^ { a } + 2 ^ { a } + \ldots + \mathrm { n } ^ { a } \right) } { ( n + 1 ) ^ { a - 1 } [ ( n a + 1 ) + ( n a + 2 ) + \ldots + ( n a + n ) ] } = \frac { 1 } { 60 }$$
Then $a =$

(A) 5

(B) 7

(C) $\frac { - 15 } { 2 }$

(D) $\frac { - 17 } { 2 }$

Paper Questions

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