Question

Вычислите: 1/2+(1/(2+4))+(1/(2+4+6))+...+(1/(2+4+6+8+...+20))

Answer 1

1/2 + 1/6 + 1/12 + 1/20 + ... +1/110 =  1/2 + (1/2-1/3)+(1/3 -1/4) +(1/4-1/5)+
+...+(1/10 -1/11)= 1/2 + 1/2 -1/11= 1 - 1/11 = 11/11 - 1/11= 10/11