1/2×2+1/4×3+1/6×4+1/8×5+…1/18×10=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 18:44:47
1/2×2+1/4×3+1/6×4+1/8×5+…1/18×10=?

1/2×2+1/4×3+1/6×4+1/8×5+…1/18×10=?
1/2×2+1/4×3+1/6×4+1/8×5+…1/18×10=?

1/2×2+1/4×3+1/6×4+1/8×5+…1/18×10=?
1/2×2+1/4×3+1/6×4+1/8×5+…1/18×10
= 1/(2*1)*2+1/(2*2)*3+1/(2*3)*4+……1/(2*9)*10
= 1/2(1/1*2+1/2*3+1/3*4+……+1/9*10)
= 1/2(1/1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10)
= 1/2(1/1-1/10)
= 9/20

懒得人`````没什么好答的

9
∑(n+1)/2n
n=1

原式
=1/2[1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)......1/(9*10)]
=1/2[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5......-1/9+1/9-1/10]
=(1/2)*(9/10)
=9/20