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JEE Advanced 2013 Paper 2 Mathematics Q5
Mathematics
Problem
For
a
∈
R
a\in\mathbb R
a
∈
R
,
a
≠
−
1
a\ne-1
a
=
−
1
,
lim
n
→
∞
1
a
+
2
a
+
⋯
+
n
a
(
n
+
1
)
a
−
1
[
(
n
a
+
1
)
+
(
n
a
+
2
)
+
⋯
+
(
n
a
+
n
)
]
=
1
60
\displaystyle\lim_{n\to\infty}\frac{1^a+2^a+\cdots+n^a}{(n+1)^{a-1}[(na+1)+(na+2)+\cdots+(na+n)]}=\frac1{60}
n
→
∞
lim
(
n
+
1
)
a
−
1
[(
na
+
1
)
+
(
na
+
2
)
+
⋯
+
(
na
+
n
)]
1
a
+
2
a
+
⋯
+
n
a
=
60
1
. Then
a
a
a
=
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