Question

does the series diverge on converge. if it converges, what is the number that it converges to. 3*(2^n-1 / 5^n)

Answer 1

\[\large {3\left( \frac{2^{n-1}}{5^n}\right)=\frac{3}{2}\cdot\frac{2\cdot 2^{n-1}}{5^n}=\frac{3}{2}\cdot\left(\frac{2}{5}\right)^n}\]
the terms of the sequence form a geometric sequence. thus the series is geometric with \(r=2/5\)