Question

Tính:\(\frac{12}{56}+\frac{12}{140}+\frac{12}{260}+...+\frac{12}{1400}\)

Answer 1

Ta đặt phép tính trên là A

A=12/56+12/140+12/260+....+12/1400

A=6/28+6/70+6/130+...+6/700 3/6

A=3/28+3/70+3/130+....+3/700 3/6.

A=3/4.7+3/7.10+3/10.13+....+3/25.28 3/6

.A=1/4-1/7+1/7-1/10+1/10-1/13+...+1/25-1/28 3/6.

A=(1/4-1/28)+(1/7-1/7)+(1/10+/10)+..+(1/25-1/28) 3/6.

A=7/28-1/28+0+0+...+0 3/6.A=3/14

A=3/14:3/6 A=3/14.6/3 A=3/7

Vậy GTBT=3/7 

Answer 2

12/56 + 12/140 + 12/260 + ... + 12/1400

= 5/28 + 5/70 + 5/130 + ... + 5/700

= 5/3 x ( 3/4x7 + 3/7x10 + 3/10x13 + ... + 3/25x28 )

= 5/3 x ( 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/25 - 1/28 )

= 5/3 x ( 1/4 - 1/28 )

= 5/3 x 3/14

= 5/14

Answer 3

ta đặt phép tính trên là A

A=12/56+12/140+12/260+....+12/1400

A=6/28+6/70+6/130+...+6/700

3/6.A=3/28+3/70+3/130+....+3/700

3/6.A=3/4.7+3/7.10+3/10.13+....+3/25.28

3/6.A=1/4-1/7+1/7-1/10+1/10-1/13+...+1/25-1/28

3/6.A=(1/4-1/28)+(1/7-1/7)+(1/10+/10)+..+(1/25-1/28)

3/6.A=7/28-1/28+0+0+...+0

3/6.A=3/14

A=3/14:3/6

A=3/14.6/3

A=3/7

Vậy GTBT=3/7