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10
2006 SMT Algebra #10 - Evaluate for |a|<1
2006 SMT Algebra #10 - Evaluate for |a|<1
Source:
August 24, 2011
ratio
geometric sequence
Problem Statement
Evaluate:
∑
k
=
1
∞
k
a
k
−
1
\sum^{\infty}_{k=1} \tfrac{k}{a^{k-1}}
∑
k
=
1
∞
a
k
−
1
k
for all
∣
a
∣
<
1
|a|<1
∣
a
∣
<
1
.
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