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1/6+1/24+1/60+.+1/720.简便方法哦~跪了
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1/6+1/24+1/60+.+1/720.简便方法哦~跪了
▼优质解答
答案和解析
an=1/n*(n+1)(n+2)
=1/2*[1/n*(n+1)-1/(n+1)(n+2)]
Sn=a1+a2+……+an
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+……1/n*(n+1)-1/(n+1)(n+2)]
=1/2[1/2-1/(n+1)(n+2)]
原式=a1+a2+……+a8
当n=8时,原式=11/45
=1/2*[1/n*(n+1)-1/(n+1)(n+2)]
Sn=a1+a2+……+an
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+……1/n*(n+1)-1/(n+1)(n+2)]
=1/2[1/2-1/(n+1)(n+2)]
原式=a1+a2+……+a8
当n=8时,原式=11/45
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