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Mathematics
Mathematics
Problem
Which of the following infinite series converges? a)
∑
n
=
1
∞
1
ln
(
n
+
1
)
\displaystyle\sum_{n=1}^{\infty}\frac{1}{\ln\!(n+1)}
n
=
1
∑
∞
ln
(
n
+
1
)
1
b)
∑
n
=
1
∞
1
n
\displaystyle\sum_{n=1}^{\infty}\frac{1}{n}
n
=
1
∑
∞
n
1
c)
∑
n
=
1
∞
1
n
3
/
2
\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^{3/2}}
n
=
1
∑
∞
n
3/2
1
d)
∑
n
=
1
∞
3
n
2
n
\displaystyle\sum_{n=1}^{\infty}\frac{3^{n}}{2^{n}}
n
=
1
∑
∞
2
n
3
n
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