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1/7×11+1/11×15+1/15×19…+1/51×55智力冲浪
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1/7×11+1/11×15+1/15×19…+1/51×55智力冲浪
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答案和解析
1/7×11+1/11×15+1/15×19…+1/51×55应该是1/(7×11)+1/(11×15)+1/(15×19)…+1/(51×55)
则有
1/(7×11)+1/(11×15)+1/(15×19)…+1/(51×55)
=1/4*[4/(7×11)+4/(11×15)+4/(15×19)…+4/(51×55)]
=1/4*(1/7-1/11+1/11-1/15+1/15-1/19+...+1/51-1/55)
=1/4*(1/7-1/55)
=1/4*[(55-7)/(55*7)]
=1/4*48/385
=12/385
则有
1/(7×11)+1/(11×15)+1/(15×19)…+1/(51×55)
=1/4*[4/(7×11)+4/(11×15)+4/(15×19)…+4/(51×55)]
=1/4*(1/7-1/11+1/11-1/15+1/15-1/19+...+1/51-1/55)
=1/4*(1/7-1/55)
=1/4*[(55-7)/(55*7)]
=1/4*48/385
=12/385
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