Question

S= 1/ 2√1+1√2+ 1 / 3√2+2√3+.....+ 1 / 100√99+99√100

Answer 1

S = 1/(2+√2) + 1/(3√2+2√3) +.....+ 1/(100√99 +99√100)=(2-√2)/2 +(3√2-2√3)/6 +.........(100√99 - 99√100)/9900 = 1- √2/2 + √2/2 - √3/3+ +...√99/99 - √100/100 = 1 - √100/100 = 1- 1/10 = 9/10 = 0,9