Question

1/1+1 + 1/1+2+3 + 1/1+2+3+4 + .+ 1/1+2+3+4+.+50 = 简便运算

Answer 1

1/1+2 + 1/1+2+3 + 1/1+2+3+4 + .+ 1/1+2+3+4+.+50

=2/2*3+2/3*4+2/4*5+...+2/50*51

=2[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/50-1/51)]

=2*(1/2-1/51)

=49/51