Answer
The series is convergent.
$\sum_{n=1}^{\infty}\frac{7^{n+1}}{10^n}=\frac{49}{3}$
Work Step by Step
The graph of the sequence of terms and the sequence of partial sums is given below.
From the graph, as $n$ becomes larger the value of $S_n$ approaches to a single value.
It appears that the series is convergent.
The series $\sum_{n=1}^\infty\frac{7^{n+1}}{10^n}$ is an infinite geometric series with the first term $a_1=\frac{49}{10}$ and the common ratio $r=\frac{7}{10}$.
Find the sum of the series:
$\sum_{n=1}^{\infty}\frac{7^{n+1}}{10^n}=\frac{a_1}{1-r}=\frac{49/10}{1-7/10}=\frac{49/10}{3/10}=\frac{49}{3}$
