Bài 1:
\(\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{97.99}\)
\(=2\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=2.\frac{32}{99}=\frac{64}{99}\)
Bài 2:
a) \(2.4^x-18=110\)
\(\Leftrightarrow2.4^x=128\)
\(\Leftrightarrow4^x=64\)
\(\Leftrightarrow4^x=4^3\Leftrightarrow x=3\)
Vậy x = 3
b) \(\left(\frac{3}{2}x-1\right)^5=1\)
\(\Leftrightarrow\frac{3}{2}x-1=1\)
\(\Leftrightarrow\frac{3}{2}x=2\)
\(\Leftrightarrow x=\frac{4}{3}\)
Vậy \(x=\frac{4}{3}\)
a) 4/3.5 + 3/5.7 + .... + 4/97.99
= 4( 1/3.5 +1/5.7 + ... + 1/97.99 )
= 4 . 1/2 . 2 ( 1/3.5 +1/5.7 + ... + 1/97.99 )
= 4/2 ( 2/3.5 + 2/5.7 + .... + 2/97.99 )
= 2 ( 5-3/3.5 + 7-5/5.7 + ..... + 99-97/97.99 )
= 2 (5/3.5 - 3/3.5 + 7/5.7 - 5/5.7 + .... + 99/97.99 - 97/97.99 )
= 2 ( 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/97 - 1/99 )
= 2 ( 1/3 -1/99 )
= 2 (33/99 - 1/99 )
= 2 . 32/99
= 32.2/99
=64/99
b) 2. 4x - 18 = 110
2. 4x = 110 + 18
2. 4x = 128
4x = 128 : 2
4x = 64
4x = 43
=> x = 3
c) ( 3/2 . x - 1 )5 = 1
( 3/2 . x - 1 )5 = 15
=> 3/2 . x - 1 = 1
3/2 . x = 1+1
3/2 . x = 2
x = 2 : 3/2
x = 2 . 2/3
x = 4/3
Nhớ cho mk nhé !!! Cảm ơn nhiều !
