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Magazine Problem 1
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=0}^{\infty} \frac{(-2)^{n}}{5^{n+1}} $$
Problem 2
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=1}^{\infty} \frac{4^{n-1}}{3^{2 n}} $$
Problem 3
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=0}^{\infty} \frac{13}{(-5)^{n}} $$
Problem 4
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=0}^{\infty}\left(-\frac{3}{2}\right)^{n} $$
Problem 5
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=0}^{\infty} e^{-0.5 n} $$
Problem 6
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=1}^{\infty} \frac{2^{n+1}}{3^{n-1}} $$
Problem 7
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=0}^{\infty}\left[\left(\frac{2}{3}\right)^{n}+\left(\frac{3}{2}\right)^{n}\right] $$
Problem 8
Determine whether the given geometric series converges or diverges. If the series converges, find its sum. $$ \sum_{n=0}^{\infty}\left(\frac{3}{2}\right)\left(\frac{2}{3}\right)^{n} $$
Problem 9
Determine whether the given series converges or diverges. $$ \sum_{n=0}^{\infty} \frac{1}{2 n+1} $$
Problem 10
Determine whether the given series converges or diverges. $$ \sum_{n=1}^{\infty}\left(1+\frac{1}{n}\right)^{2} $$
