Everything Cancels Off, Right?

Calculus Level 1

Does the infinite product $\prod_{k=1}^\infty\frac{k+1}{k}$ converge to a finite value?

Yes No

2 solutions

Chew-Seong Cheong
Jan 17, 2016

$\begin{aligned} \prod_{k=1}^n \frac{k+1}{k} & = \frac{(n+1)!}{n!} = n +1 \\ \Rightarrow \lim_{n \to \infty} \prod_{k=1}^n \frac{k+1}{k} & = \infty \end{aligned}$

$\boxed{\text{No}}$ , it does not converge.

Hamza A
Jan 17, 2016

Everything Cancels Off, Right?

2 solutions

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