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1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55=?请高手多出几道这类型的题,带解说最好
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1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55=?请高手多出几道这类型的题,带解说最好
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答案和解析
1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55
1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55
=2×（1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110)
=2x(1/1*2=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/9*10+1/10*11)
=2x(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11)
=2x(1-1/11)
=20/11
1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55
=2×（1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110)
=2x(1/1*2=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/9*10+1/10*11)
=2x(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11)
=2x(1-1/11)
=20/11
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