Question

How do you test the series for convergence or divergence for `sum (-1)^n n / 10^n` from n=1 to infinity?

Answer 1

Series is absolutely convergent.

Apply root test, L= lim n`->` `oo` `abs(a_(n+1)/a_n`

=lim n`->oo` `abs ((n+1)/10^(n+1)*10^n /n`

=lim n`->oo` `abs(1+1/n)*1/10`

=`1/10`

L= `1/10` < 1

Hence the series would converge