1. Tính: 1/2+ 1/3+ 1/6+ 1/10+1/15+....+ 1/36+ 1/45
....
A+1/2=1/1+ 1/3+ 1/6+ 1/10+1/15+....+ 1/36+ 1/45

xet mau vp
1=1
3=1+2
6=1+2+3
10=1+2+...+4
15=1+2+...+5
45=1+2...+9
Bn=n(n+1)/2
1/Bn =2/[n(n+1)]=2[1/n-1/(n+1)]
(A+1/2)/2=(1/1-1/2)+(1/2-1/3)+...+(1/9+1/10)
(A+1/2)/2=1-1/10
A+1/2=2-1/5
A=2-(1/2+1/5)
A=2-7/10=13/10

1. Đặt A = 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45 <=> 1/2 . A = 1/2.( 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45) <=> 1/2 . A = 1/4 + 1/6 +1/12 +1/20 +1/30 + . . . + 1/72 +1/90 <=> 1/2 . A + 3/4 = 1 + 1/6 +1/12 +1/20 +1/30 + . . . + 1/72 +1/90 <=> 1/2 . A + 3/4 = 1 - 1/10 <=> A = 3/10