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

Definite Integration

JEE Main 2017 · 9 Apr, Morning shift · Q3284

MathematicsHard210×since 2002Q3284

\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 · 9 Apr, Morning shift · Q3284

MathematicsHard210×since 2002Q3284

\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 :