Question

计算题，求解

1/1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+…+1/10+…+10/10

Answer 1

32.5

1+2+3+……+n=n*(n+1)/2

1+2+3+……+n/n=(n+1)/2

原式=(2+3+……+11)/2

=32.5

Answer 2

Answer 3

=1/1 + (1+2)/2 + (1+2+3)/3 + (1+2+3+4)/4+...+(1+2+...+10)/10
按照等差数列公式1+2+...+n = n(1+n)/2
则（1+2+...+n)/n = (1+n)/2
所以，等式
= (1+1)/2 + (1+2）/2 + (1+3)/2+...+(1+10)/2
= 1/2 x 10 + (1+2+3+...+10)/2
= 5 + [10x(1+10)/2]/2
= 5 + 27.5
=32.5

Answer 4

an
= (1+2+...+n)/n
= (n+1)/2
Sn

=a1+a2+...+an
=(1/2) [n( 2+(n+1) )/2]
=(1/4)n(n+3)
1/1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4+…+1/10+…+10/10
=S10
=(1/4)(10)(13)
=65/2

Answer 5

原式=1+（1+1/2）+（1+1）+（1+3/2）+……+（1+9/2）
=10(1+1+9/2)/2
=65/2.