计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)

问题描述:

计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)

1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)
=[1/x - 1/(x+1)] +[1/(x+1) - 1/(x+2) ]+.+[1/(x+99) - 1/(x+100)]
=1/x - 1//(x+100)
=100/x(x+100)