(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 07:00:57
(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
xP;0 ".p TLT03ӭ7AеWqR VJl?lP)sFXqSRUUaZȮ`an0bH3E+G?`l(vRQb<{/]\HAXإwjX?E+5{)D r i?'$$¹WJ<# oR

(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)

(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
1/2+1/6=2/3
1/2+1/6+1/12=3/4
1/2+1/6+1/12+1/20=4/5
.
所以
1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
=2011/2012

2011/2012

1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2011-1/2012
=1-1/2012
=2011/2012

2011/2012

1/n(n+1)=1/n-1/(n+1)
1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2011-1/2012
=1-1/2012
=2011/2012