Math Olympiad | Find the sum without using a Calculator | VIJAY Maths

The easiest way is

1/(x(x+1))=(1/x)-(1/(x+1))

Nice information,example

Excellent

asnwer=1 isit

👍👍👍

Magic ;)

Nice question 🎉🎉❤

1/28+1/36+1/45+1/55+1/66+1/78+1/91+1/105/ 4950+ /2^2^3+/3^3^3+/4^2^3+/2^3^2^3+/3^3^3^3+/7^2^3+/30^61/+/1^2^3+/4^3^2^2^3+/1^1^1^1+/1^1^1+/2^2^1^1^1+/1^1^1^1+/1^1^1^1+/3^4^1^1^1+/30^30^31+/1^1^1+/2^2^1^1^1^1+/1^1+/3^2^2^1+/1^1^1^1+/1^1+/3^1^2^1 +/3^2(n ➖ 3n+2).

2*(1/7*8+1/8*9+1/9*10+...+1/99*100)=
2*[(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+...+(1/99-1/100)]=
2*[1/7-1/8+1/8-1/9+1/9-1/10+...+1/98-1/99+1/99-1/100)
=2*(1/7-1/100)=2(93/700)=93/350
=2/7

I'm pretty sure I was never taught the formula 1/(ab)=1/(b-a)*(1/a-1/b). Did I just forget? If so, when do students learn that formula?