1/(1*3)+1/(3*5)+1/(5*7)+.+1/(49+51)的简便运算

问题描述:

1/(1*3)+1/(3*5)+1/(5*7)+.+1/(49+51)的简便运算

1/(1*3)+1/(3*5)+1/(5*7)+.+1/(49*51)
=(1-1/3+1/3-1/5+1/5-1/7+.+1/49-1/51)/2
=(1-1/51)/2
=25/51