1/1*2+1/2*4+1/3*5+1/4*6+…+1/n*(n+2)用简便方式法计算将分数拆项
问题描述:
1/1*2+1/2*4+1/3*5+1/4*6+…+1/n*(n+2)用简便方式法计算将分数拆项
答
一般地,1 / [n*(n+2)] = 0.5 * [1/n - 1/(n+2)]
所以
1/1*2 + 1/2*4 + 1/3*5 + 1/4*6 +…+ 1/n*(n+2)
=0.5[ 1 - 1/2] + 0.5[1/2 - 1/4 ] + 0.5[1/4 - 1/6] + .+ 0.5 * [1/n - 1/(n+2)]
=0.5 [1 - 1/(n+2)]
=(n+1)/ [ 2(n+2)]