数列裂项求和sn=1/(1+2)+1/(1+2+3)+~+1/(1+2+3+~+n)

来源:学生作业帮助网 编辑:作业帮 时间:2024/08/30 10:46:58
数列裂项求和sn=1/(1+2)+1/(1+2+3)+~+1/(1+2+3+~+n)
x){6uӎ/7\Ʀzl 5 4!v di$铫UΆ"{hC}#]C}{$efY`)edyy@=y =`Ӑ35B/.H̳z9Q2 γ67Vx1n+@>wÔv>

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)