Question

1/6+1/12+1/20+1/30 ...............+1/9900= ?

Answer 1

Step-by-step explanation:

1/2+1/6+1/12+1/20+..............+1/9900 note that the numbers 2,6,12,20,......,9900 are of the form n(n+1) so, nth term Tn = 1/n(n+1) = 1/n - 1/(n+1) so, the series is 1/1-1/2+1/2-1/3+1/3-1/4+.................-1/99+1/99-1/100 = 1 - 1/100 = 99/100