The question:
Test the following series for convergence or divergence: $$ \frac{1!}{10}-\frac{2!}{10^2}+\frac{3!}{10^3}-\frac{4!}{10^4}+\cdots $$ My answer:
The general term is then $$ \sum_{n=1}^\infty\frac{(-1)^{n-1}n!}{10^n} $$ and using the alternating series test $u_{n+1}
for $n=1$:$u_n=0.1$
for $n=2$:$u_n=0.02$
for $n=3$:$u_n=0.006$
for $n=4$:$u_n=0.0024$
$\cdots$
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