1/n(n+1)(n+2)求和怎么做
题目
1/n(n+1)(n+2)求和怎么做
答案
1/n(n+1)(n+2)
=1/2[2/n(n+1)(n+2)]
=1/2[(n+2)-n]/n(n+1)(n+2)]
=(1/2)[(n+2)/n(n+1)(n+2)-n/n(n+1)(n+2)]
=(1/2)[1/n(n+1)-1/(n+1)(n+2)]
所以和=(1/2)[1/1*2-1/2*3+1/2*3-1/3*4+……+1/n(n+1)-1/(n+1)(n+2)]
=(1/2)[1/1*2-1/(n+1)(n+2)]
=n(n+3)/[4(n+1)(n+2)]
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