Bài 1:
a) `1/n - 1/(n+1) = (n+1)/(n(n+1)) - n/(n(n+1)) = (n+1-n)/(n(n+1))= 1/(n(n+1))`
b) `1/1.2 + 1/2.3 + 1/3.4`
`= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4`
`= 1 - 1/4`
`= 4/4 -1/4 `
`=3/4`
c) `1/1.2+ 1/2.3 +...+ 1/99.100`
`= 1 - 1/2 + 1/2-1/3+...+ 1/99 - 1/100`
`= 1 - 1/100`
`= 99/100`
Bài 2:
a)`2^(x+2) =8^5`
`=> 2^(x+2) = (2^3)^5`
`=> 2^(x+2) = 2^15`
`=> x+2 =15`
`=> x=15-2`
`=> x=13`
Vậy `x=13`
b) `3/5 x -2/9 = 1- 2/5`
`=> 3/5 x - 2/9 = 5/5 - 2/5`
`=> 3/5 x - 2/9 = 3/5`
`=> 3/5 x =3/5 + 2/9`
`=> 3/5 x= 37/45`
`=>x =37/45 : 3/5`
`=> x= 37/45 . 5/3`
`=> x= 37/27`
Vậy `x= 37/27`
c) `10^x /2^x =125`
`=> 10^x : 2^x = 125`
`=> 5^x =125`
`=> 5^x = 5^3`
`=> x=3`
Vậy `x=3`
