Question

请教高一数学，（题目中的分子都为1），请列步骤。谢谢

Answer 1

字就不吐槽了。。还是不懂问我

Answer 2

追问

请问这步提取公因数1/2时，带字母n 的几项如何得到。请指教

追答

Answer 3

1/[(n+1)²-1]=1/(n²+2n)=1/[n(n+2)]=(1/2)*[(1/n)-(1/n+2)]
所以：
原式=(1/2)*[1-(1/3)]+(1/2)*[(1/2)-(1/4)]+(1/2)*[(1/3)-(1/5)]+……+(1/2)*[(1/n-2)-(1/n)]+(1/2)*[(1/n-1)-(1/n+1)]+(1/2)*[(1/n)-(1/n+2)]

=(1/2)*[1-(1/3)+(1/2)-(1/4)+(1/3)-(1/5)+……+(1/n-2)-(1/n)+(1/n-1)-(1/n+1)+(1/n)-(1/n+2)]

=(1/2)*[1+(1/2)-(1/n+1)-(1/n+2)]

=(3/4)-(1/2)*[(2n+3)/(n+1)(n+2)]

Answer 4

(n+1)^2-1=(n+1+1)(n+1-1)=n(n+2)

1/[n(n+2)]=1/2 [1/n- 1/(n+2)]

每个都这么代进去，把1/2提出来：

1/2 [(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+……+(1/(n-1)-1/(n+1))+(1/n-1/(n+2))+(1/(n+1)-1(n+3))]

注意，中间很多项正好一正一负，都可以消去，只剩下头两项正的后两项负的

1/2 [ 1/2+1/3-1/(n+2)-1/(n+3)]

Answer 5