For the given series the ratio of (n+1)-th term to n-th term is constant which is
Hence, the terms of the given series are in geometric progression.
Write the given series in standard geometric series form.
The general geometric series,
, where a is the first term and r is the common ratio
converges to , for -1<r<1
Otherwise it diverges.
Compare the series with the general geometric series, to get
Plug in equation (1), to get
Not exactly what you’re looking for?