Question

简便运算！急急急!!!在线等

1/2²-1+1/4²-1+1/6²-1+......+1/100²-1

Answer 1

1/2²-1+1/4²-1+1/6²-1+......+1/100²-1

=1/(1×3)+1/(3×5)+1/(5×7)+...+1/(99×101)
=1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101
=1-1/101
=100/101;

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可答案是50/101

追答

1/2²-1+1/4²-1+1/6²-1+......+1/100²-1

=1/(1×3)+1/(3×5)+1/(5×7)+...+1/(99×101)
=(1/2)[1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101]
=(1/2)[1-1/101]
=(1/2)[100/101];
=50/101

对的；我漏乘了1/2