What is the sum from k=0 to infinity of (2^k)/(k!) ?

The sum from k=0 to infinity of (2^k)/(k!) is converges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from k=0 to infinity of (2^k)/(k!)

k = 0 \sum \infty \frac{2 ^{k}}{k !}

converges

Solution steps

k = 0 \sum \infty \frac{2 ^{k}}{k !}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{0. 5 ^{n}}{n}

n = 0 \sum \infty \frac{2 ^{2 n}}{n !}

n = 1 \sum \infty e^{0 n}

n = 1 \sum \infty n! e^{- 8 n}

n = 1 \sum \infty \frac{1}{n + sin ( n )}

What is the sum from k=0 to infinity of (2^k)/(k!) ?
The sum from k=0 to infinity of (2^k)/(k!) is converges