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5
I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 5
I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 5
Source:
April 10, 2012
limit
calculus
calculus computations
Problem Statement
Let
a
1
>
a
2
>
.
.
.
.
.
>
a
r
a_1>a_2>.....>a_r
a
1
>
a
2
>
.....
>
a
r
be positive real numbers . Compute
lim
n
→
∞
(
a
1
n
+
a
2
n
+
.
.
.
.
.
+
a
r
n
)
1
n
\lim_{n\to \infty} (a_1^n+a_2^n+.....+a_r^n)^{\frac{1}{n}}
lim
n
→
∞
(
a
1
n
+
a
2
n
+
.....
+
a
r
n
)
n
1
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