计算：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)

2008foreverlove 1年前 已收到2个回答 举报
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无身无色 幼苗

共回答了11个问题采纳率：72.7% 举报

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+9)-1/(x+10)
=1/x-1/(x+10)
=(x+10-x)/{x(x+10)}
= 10/{x(x+10)}

1年前

3

yqjf_c55xt_66bd 花朵

共回答了2704个问题 举报

1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+...+1/[(x+9)(x+10)]
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)
=1/x-1/(x+10)
=(x+10-x)/[x(x+10)]
=10/[x(x+10)]

1年前

0
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