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Mathematics
Mathematics
Problem
Determine the value of the series
∑
k
=
2
∞
1
k
(
k
−
1
)
\displaystyle \sum_{k=2}^{\infty} \frac{1}{k(k-1)}
k
=
2
∑
∞
k
(
k
−
1
)
1
. a)
0
0
0
b)
1
1
1
c)
ln
2
\ln 2
ln
2
d) It diverges without bound.
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