найти сумму: 1/2+1/6+1/12+1/(4*5)+1/(5*6)+1/(6*7)+...+1/(49*50)=?

Question

найти сумму: 1/2+1/6+1/12+1/(4*5)+1/(5*6)+1/(6*7)+...+1/(49*50)=?

Answer 1

1/(1*2)=1/1-1/2

1/(2*3)=1/2-1/3

...

1/(49*50)=1/49-1/50

 

Сумма равна 1-1/50=49/50