Thread: sum fof series?

How do we find the sum of the below series:
a)
1 + 1/3 + 1/6 + 1/10 + 1/15 + .........
b)
1/2 + 1/6 + 1/12 + 1/20 + ......

Thanks!!!

Originally Posted by a69356

How do we find the sum of the below series:
a)
1 + 1/3 + 1/6 + 1/10 + 1/15 + .........
b)
1/2 + 1/6 + 1/12 + 1/20 + ......

Thanks!!!

(b) $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n(n+1)} = \sum_{n=1}^{\infty} \frac{1}{n} - \frac{1}{n+1} = $

$\displaystyle \left(1 - \frac{1}{2}\right) + \left(\frac{1}{2} - \frac{1}{3}\right) + ... + \left(\frac{1}{n-1} - \frac{1}{n}\right) + \left(\frac{1}{n} - \frac{1}{n+1}\right) + ... = $

$\displaystyle \lim_{n \to \infty} 1 - \frac{1}{n+1} = 1$


the series in (a) is just twice the sum of (b).