$$\sum_{n=1}^{\infty}{(7)^{n} }$$

asked by guest
on Oct 22, 2024 at 6:15 am



You asked:

Evaluate the expression: \(\sum_{n = 1}^{\infty} {{7}^{n}}\)

MathBot Answer:

The infinite series \(\displaystyle\sum_{n=1}^{\infty} 7^{n}\) diverges.


We can use the nth-term test to determine convergence of this series.

Given a series \(\displaystyle\sum a_n\), if \(\displaystyle\lim_{n \to \infty}a_n \neq 0\) or does not exist, then the series diverges.
This test cannot prove convergence.

\(\displaystyle\lim_{n \to \infty} 7^{n}\) does not exist.

Therefore the series diverges.