If lim n → ∞ (1^(a) + 2^(a) +...... + n^(a))/((n + 1)^(a - 1)[ (na + 1) + (na + 2) +..... + (na + n) ]) = 1/60 for some positive real number a, then a is equal to:

Integral Calculus: JEE Main 2017 Mathematics question

JEE Main 2017 · 9 Apr, Morning shift · Q3284

JEE Main 20179 Apr, Morning shiftMathematicsHardIntegral Calculus369× since 2002

\mathop {\lim }\limits_{n \to \infty } \,\,{{{1^a} + {2^a} + ...... + {n^a}} \over {{{(n + 1)}^{a - 1}}\left[ {\left( {na + 1} \right) + \left( {na + 2} \right) + ..... + \left( {na + n} \right)} \right]}} = {1 \over {60}}

for some positive real number a, then a is equal to :

JEE Main 2017 Integral Calculus Question with Solution (9 Apr Morning shift, Q3284) | JEE Arc

JEE Main 2017 · 9 Apr, Morning shift · Q3284

JEE Main 20179 Apr, Morning shiftMathematicsHardIntegral Calculus369× since 2002

\mathop {\lim }\limits_{n \to \infty } \,\,{{{1^a} + {2^a} + ...... + {n^a}} \over {{{(n + 1)}^{a - 1}}\left[ {\left( {na + 1} \right) + \left( {na + 2} \right) + ..... + \left( {na + n} \right)} \right]}} = {1 \over {60}}

for some positive real number a, then a is equal to :