Question

1/2×4+1/3×5+1/4×6+1/5×7+……+1/8×10+1/9×11 数学题

Answer 1

以上数为列求和，每个数的分母都能写成n(n+2)即算式中每个数都可写作1/n(n+2) 其中n=2，3，4，5，6，7，8，9
因2/n(n+2)=（n+2-n)/（n(n+2)）=(1/n)-(1/（n+2 ）)
所以原式=（1/2-1/4+1/3-1/5+1/4-1/6+...+1/9-1/11)/2
=(1/2+1/3-1/10-1/11)/2
=53/165

Answer 2

原式=1/2(1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+...+1/8-1/10+1/9-1/11)
=1/2(1/2+1/3-1/10-1/11)
=53/165

Answer 3

1/2X(2+2)+1/3X(3+2)+1/4X(4+2)+……+1/8(8+2)+1/9(9+2)
=8+2(1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9)
=8+2(1/2+1/3+1/6+1/4+1/8+1/5+1/7+1/9)
=8+2(1+3/8+1/5+1/7+1/9)
=10+2(3/8+1/5+1/7+1/9)到这就要自己算数啦
=10+2*(2089/2520)
=10+2089/1260
=14689/1260,

Answer 4

原式=1/2(1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+...+1/8-1/10+1/9-1/11)
=1/2(1/2+1/3-1/10-1/11)
=53/165

Answer 5

=53/165