Make sure you watch the video first

Algebra Level 3

Before you begin this problem, take a moment to familiarize yourself with how big Graham's number is from its Wikipedia page or from a video by Numberphile , featuring Ronald Graham himself.

Let $G$ be equal to Graham's number. In which of the following ranges does the value of $\displaystyle\sum_{n=G}^\infty\dfrac{1}{n}$ fall?

None of these

(0,1]

(1,\pi]

(\pi,G]

1 solution

Daniel Liu
Sep 25, 2014

We know that $\sum\dfrac{1}{n}$ is infinite.

Also, $\displaystyle\sum_{n=1}^{G-1}\dfrac{1}{n}$ is finite.

Therefore, $\sum\dfrac{1}{n}-\displaystyle\sum_{n=1}^{G-1}\dfrac{1}{n}=\sum_{n=G}^{\infty}\dfrac{1}{n}$ is infinite.

Make sure you watch the video first

1 solution

0 pending reports