Question

难倒小学老师的小学问题：1又1/2+2又1/6+3又1/12+4又1/20+……+10又1/110

计算题 写清过程

Answer 1

1又1/2+2又1/6+3又1/12+4又1/20+……+10又1/110
=(1+1/2)+(2+1/6)+..+(10+1/110)
=1+2+..+10+((1-1/2)+(1/2-1/3)+..+(1/10-1/11))
=55+1-1/2+1/2-1/3+..+1/9-1/10+1/10-1/11
=55+10/11
=55又10/11

Answer 2

1又1/2+2又1/6+3又1/12+4又1/20+……+10又1/110
=(1+2+3+...+10)+[(1/2)+(1/6)+(1/12)+...+(1/110)]
=(1+10)*10/2+[1/(1*2)+1/(2*3)+1/(3*4)+...+1/(10*11)]
=55+[(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/10)-(1/11)]
=55+[1-(1/11)]
=55+10/11
=615/11.

Answer 3

通式为n+1/[n(n+1)]=n+1/n-1/n+1
1+1/2=1+1-1/2
2+1/6=2+1/2-1/3
3+1/12=3+1/3-1/4
4+1/20=4+1/4-1/5
....
9+1/90=9+1/9-1/10
10+1/110=10+1/10-1/11
左边相加=右边相加=5(1+10)+1-1/11=55+10/11=55又10/11

Answer 4

原式=1+2+3+4+5+6+7+8+9+10+1/2+1/6+......+1/110
=55+(1/1-1/2)+(1/2-1/3)+.......+(1/10-1/11)
=55+1-1/11
=55又10/11

Answer 5

1/[(N+1)N]=1/N-1/(N-1)
所以原式=1+2+3+4+5+6+7+8+9+10+1/2+1/[2*3]+1/3*4……+/10*11
=55+1-1/2+1/2-1/3+1/3-1/4+……+1/10-1/11
=55又10/11