Question

[huỳnh thị thu uyên]

tính nhanh : C = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90

Answer 1

[Nguyễn Nam Cao]

1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90 

= 1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90

= 9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90) 

= 9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)] 

= 9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)

=9 – (1 – 1/10) = 9 – 9/10 = 81/10

Answer 2

[Nguyễn Nam Cao]

1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110

= 1 - 1/2 + 1 - 1/6 + 1 - 1/12 .....+1 - 1/110

= 10 - ( 1/2 + 1/6 + ...+ 1/110)

= 10 - ( 1 - 1/ 2+ 1/2 - 1/ 3+ 1/3 - 1/4 ....+ 1/10 - 1/11)

= 10 - (1 - 1/11)= 10 - 10/11

= 100/11