Question

cho A=1/3+1/6+1/10+1/15+........+1/91+1/105

So sánh A với 1

 

Answer 1

nhân 2 vế với 1/2 ta có

1/2 x A = 1/2 x (1/3 + 1/6 +1/10 + 1/15 + .......+1/91 + 1/105 )

1/2 x A = 1/6 +1/12 + 1/20 + 1/30 + ...............+1/182 + 1/210

1/2 x A = 1/(2x3) + 1/(3x4) + 1/(4x5) + 1/(5x6) +................+1/(13x14) + 1/(14x15)

1/2 x A = 1/2 - 1/3 +1/3 -1/4 + 1/4 - 1/5  +1/5 - 1/6+.........+1/13 - 1/14 + 1/14 - 1/15

1/2 x A = 1/2 - 1/15 =13/30

=> A = 13/30 : 1/2=13/15 <1