数列裂项求和sn=1/(1+2)+1/(1+2+3)+~+1/(1+2+3+~+n)
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数列裂项求和sn=1/(1+2)+1/(1+2+3)+~+1/(1+2+3+~+n)
数列裂项求和sn=1/(1+2)+1/(1+2+3)+~+1/(1+2+3+~+n)
数列裂项求和sn=1/(1+2)+1/(1+2+3)+~+1/(1+2+3+~+n)
原式=2×[1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+.+1/n-1/(n+1)]
=2×[1/2-1/(n+1)]
=1-2/(n+1)
1+2+……+n=n(n+1)/2
则原式=2×[1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+......+1/n-1/(n+1)]
=2×[1/2-1/(n+1)]
=1-2/(n+1)
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