1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21结果是多少?要用简便运算哦,...越快越好_数学解答

1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21结果是多少?
要用简便运算哦,...越快越好

人气：457 ℃　时间：2020-02-03 02:14:41

解答

1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21
=1/2(1-1/3+1/3-1/5+1/5-.-1/21)
=1/2*20/21
=10/21
1/N*(N+2)=1/2(1/N-1/(N+2))