a: \(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{-2}{6}=\dfrac{-1}{3}\)

b: \(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)

Đề bài yêu cầu gì?

a, Giải:

Đặt A = \(5+5^2+5^3+...+5^{99}\)

5A = \(5^2+5^3+...+5^{100}\)

5A - A = ( \(5^2+5^3+...+5^{100}\)) - ( \(5+5^2+5^3+...+5^{99}\))

4A = \(5^{100}-5\)

A = \(\frac{5^{100}-5}{4}\)

b, Giải:

Đặt B = \(\frac{1}{1.5}+\frac{1}{5.9}+...+\frac{1}{17.21}\)

4B = 4. (\(\frac{1}{1.5}+\frac{1}{5.9}+...+\frac{1}{17.21}\))

4B = \(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{17.21}\)

4B = \(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{17}-\frac{1}{21}\)

4B = 1 - \(\frac{1}{21}\)

4B = 20/21

B = \(\frac{\frac{20}{21}}{4}\) = 5/21

\(a,\dfrac{3}{5}+\dfrac{3}{5\cdot9}+\dfrac{3}{9\cdot13}+....+\dfrac{3}{97\cdot101}\)

\(=\dfrac{3}{4}\cdot\left(\dfrac{4}{5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+....+\dfrac{4}{97\cdot101}\right)\)

\(=\dfrac{3}{4}\cdot\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+....+\dfrac{1}{97}-\dfrac{1}{101}\right)\)

\(=\dfrac{3}{4}\cdot\left(1-\dfrac{1}{101}\right)\)

\(=\dfrac{3}{4}\cdot\dfrac{100}{101}\)

\(=\dfrac{75}{101}\)

\(b,\left(1+\dfrac{1}{2}\right)\cdot\left(1+\dfrac{1}{3}\right)\cdot\left(1+\dfrac{1}{4}\right)\cdot....\cdot\left(1+\dfrac{1}{99}\right)\)

\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot....\cdot\dfrac{100}{99}\)

\(=\dfrac{100}{2}=50\)

Tính nhanh:

a) \(\dfrac{3}{5}+\dfrac{3}{5.9}+\dfrac{3}{9.13}+...+\dfrac{3}{97.101}\)

= \(\dfrac{3}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{101}\right)\)

= \(\dfrac{3}{4}\left(1-\dfrac{1}{101}\right)\)

= \(\dfrac{3}{4}\times\dfrac{100}{101}\)

= \(\dfrac{75}{101}\)

b) \(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)...\left(\dfrac{1}{98}+1\right)\left(\dfrac{1}{99}+1\right)\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{99}{98}.\dfrac{100}{99}\)

\(=\dfrac{3.4.5...99.100}{2.3.4...98.99}\)

\(=\dfrac{100}{2}\)

\(=50\)

\(2x=5.9^2:8\)

\(2x=5.81:8\)

\(16x=405\)

\(x=\dfrac{405}{16}\)

\(5\cdot9^2:8=2x\\\Rightarrow 2x=5\cdot81:8\\\Rightarrow2x=405:8\\\Rightarrow2x=\dfrac{405}{8}\\\Rightarrow x=\dfrac{405}{16}\\Vậy:x=\dfrac{405}{16}\)

`2.x-49=5.9`

`=> 2.x-49=45`

`=>2.x=45+49`

`=>2.x=94`

`=>x=94:2`

`=>x=47`

2 . x - 49 = 45 

2 . x = 49 + 45 

2 . x = 94 

   x = 94 : 2

  x = 47