4) `1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56`
`= 1/(1 xx 2) + 1/(2 xx3) + 1/(3 xx 4) + 1/(4 xx5) + 1/(5 xx 6) + 1/(6 xx 7) + 1/(7 xx 8)`
`= 1 - 1/2 + 1/2 - 1/3 +....+ 1/7 - 1/8`
`= 1 - 1/8`
`= 8/8 -1/8`
`= 7/8`
5) Đặt `A= 1/(1xx3) + 1/(3 xx5) + 1/(5 xx7) +...+ 1/(19 xx21)`
`2 xx A = 2( 1/(1xx3) + 1/(3 xx5) + 1/(5 xx7) +...+ 1/(19 xx21))`
`2 xx A = 2/(1xx3) + 2/(3 xx5) + 2/(5 xx7)+...+ 2/(19 xx21)`
`2 xx A = 1 - 1/3 + 1/3 - 1/5 +...+ 1/19 - 1/21`
`2xx A = 1 - 1/21`
`2xx A = 21/21 - 1/21`
`2xx A = 20/21`
`A= 20/21 : 2`
`A= 20/21 . 1/2`
`A= 10/21`
Vậy `A=10/21`
6) Đặt `A = 5/(1xx3) + 5/( 3 xx5) + 5/(5 xx7) +...+5/(19 xx21)`
`A= 5( 1/(1xx3)+ 1/(3 xx5) + ...+ 1/(19 xx21))`
`A/5 xx 2 = 2/(1 xx3) + 2/(3 xx5) +...+ 2/(19 xx21)`
`A/5 xx 2 = 1 - 1/3 + 1/3 - 1/5 +...+ 1/19 - 1/21`
`A/5 xx 2 = 1 - 1/21`
`A/5 xx 2 = 20/21`
`A = 20/21 : 2 .5`
`A = 10/21 .5`
`A= 50/21`
Vậy `A= 50/21`