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
问题描述：
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
答
1/(n-1)(n+1)
=1/2 (1/(n-1) - 1/(n+1) )
所以原式= 10/21
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))