Find-the-values-of-the-following-infinite-sum-1-3-pi-3-pi-2-3-pi-3-3-pi-4-3-pi-5-Mastermind-

Question Number 174500 by Mastermind last updated on 02/Aug/22

Find the values of the following infinite

sum :

1 + \frac{3}{π} + \frac{3}{π^{2}} + \frac{3}{π^{3}} + \frac{3}{π^{4}} + \frac{3}{π^{5}} + \dots

Mastermind

Answered by Lordose last updated on 02/Aug/22

I = 1 + \frac{3}{π} + \frac{3}{π^{2}} + \frac{3}{π^{3}} + \cdot \cdot \cdot

I = 3 \underset{k = 0}{\sum^{\infty}} \frac{1}{π^{k}} - 2

I = 3 (\frac{1}{1 - \frac{1}{π}}) - 2 = \frac{3 π}{π - 1} - 2 ▴ ▴ ▴

Commented by Mastermind last updated on 02/Aug/22

Thanks, but what is the meaning of

triangle symbol ?