a=1,b=3,求1/ab+1/(a+2)(b+2 - 知识问答

a=1,b=3,求1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.1/(a+100)(b+100)的值.

2个回答

原式=1/2(1/a-1/b)+1/2[1/(a+2)-1/(b+2)].
=1/2[1/a-1/b+1/(a+2)-1/(b+2)...+1/(a+100)-1/(b+100)
=1/2[1/a-1/(b+100)]
=1/2[1-1/103]
=51/103
下面那个横线：1/k[1/n-1/(n+k)]
k有意义

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