Question: Sum of the series S = 1 +$\frac{1}{2}$ (1 + 2) +$\frac{1}{3}$ (1 + 2 + 3) + $\frac{1}{4}$ (1 +...

Question

Sum of the series S = 1 + $\frac{1}{2}$ (1 + 2) + $\frac{1}{3}$ (1 + 2 + 3) + $\frac{1}{4}$ (1 + 2 + 3 + 4) …….. up to 20 terms is

Answer 1

t_r = $\frac{1}{r}$ (1 + 2 + 3 ….. + r) = $\frac{1}{r}.\frac{1}{2}$ r (r + 1)

S = åt_r = $\frac{1}{2}\sum_{r = 1}^{n}{(r + 1)}$ = 115

Question: Sum of the series S = 1 +\(\frac{1}{2}\) (1 + 2) +\(\frac{1}{3}\) (1 + 2 + 3) + \(\frac{1}{4}\) (1 +...