2^2/1*3+4^2/3*5+6^2/5*7+.+20^2/19*21

问题描述:

2^2/1*3+4^2/3*5+6^2/5*7+.+20^2/19*21
^是平方号,*是乘.

2^2/1*3+4^2/3*5+6^2/5*7+.+20^2/19*21
=(1+1/(1*3))+(1+1/(3*5)) +.+(1+1/(19*21))
=10+{1/(1*3)+.+1/(19*21)}
=10+{1-1/3+1/3-1/5+.+1/19-1/21}/2
=10+10/21