- #1
Chandasouk
- 165
- 0
I was asked to evaluate the summation of [tex]\frac{1}{n(n+1)}[/tex] from n=1 to infinity
I used partial fractions to obtain [tex]\frac{1}{n}[/tex] - [tex]\frac{1}{n+1}[/tex]
From here I don't understand how to evaluate. In my solutions manual, they plugged in values from 1 to infinity showing (1 - 1/2+ (1/2 - 1/3)...etc and created a new series called Sn = 1 - [tex]\frac{1}{n+1}[/tex] then took the limit of that to infinity to get the answer 1.
How would I know what Sn should be?
I used partial fractions to obtain [tex]\frac{1}{n}[/tex] - [tex]\frac{1}{n+1}[/tex]
From here I don't understand how to evaluate. In my solutions manual, they plugged in values from 1 to infinity showing (1 - 1/2+ (1/2 - 1/3)...etc and created a new series called Sn = 1 - [tex]\frac{1}{n+1}[/tex] then took the limit of that to infinity to get the answer 1.
How would I know what Sn should be?