Giải ko cần sử dụng nhị thức Newton:

\(S=5+2.5^2+3.5^3+...+49.5^{49}+50.5^{50}\)

\(\Rightarrow5S=5^2+2.5^3+3.5^4+...+49.5^{50}+50.5^{51}\)

Trừ dưới cho trên:

\(4S=-5-5^2-5^3-5^4-...-5^{50}+50.5^{51}\)

\(\Rightarrow4S=5.5^{51}-\left(5+5^2+...+5^{50}\right)\)

Chú ý rằng trong ngoặc là tổng cấp số nhân với \(\left\{{}\begin{matrix}u_1=5\\q=5\end{matrix}\right.\)

\(\Rightarrow4S=5.5^{51}-\frac{5^{51}-5}{4}=\frac{19}{4}.5^{51}+\frac{5}{4}\)

\(\Rightarrow S=\frac{19.5^{51}+5}{16}\)

50,5:2,5=20,2

kết bạn nhé

50,5 : 2,5= 20,2

50,5:2,5=20,2

\(x^2\left(x+4,5\right)=13,5\)

<=>\(x^3+4,5x^2-13,5=0\)

<=> \(x^3+3x^2+1,5x^2+4,5x-4,5x-13,5=0\)

<=>\(x^2\left(x+3\right)+1,5x\left(x+3\right)-4,5\left(x+3\right)=0\)

<=>\(\left(x+3\right)\left(x^2+1,5x-4,5\right)=0\)

<=>\(\left(x+3\right)\left[x^2+3x-1,5-4,5\right]=0\)

<=>\(\left(x+3\right)\left[x\left(x+3\right)-1,5\left(x+3\right)\right]=0\)

<=>\(\left(x+3\right)^2\left(x-1,5\right)=0\)

<=> \(\left[{}\begin{matrix}\left(x+3\right)^2=0\\x-1,5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=1,5\end{matrix}\right.\)

Vậy...

Ta có: \(x^2\left(x+4.5\right)=13.5\)

\(\Leftrightarrow x^3+\dfrac{9}{2}x^2-\dfrac{27}{2}=0\)

\(\Leftrightarrow2x^3+9x^2-27=0\)

\(\Leftrightarrow2x^3-3x^2+12x^2-18x+18x-27=0\)

\(\Leftrightarrow x^2\left(2x-3\right)+12x\left(2x-3\right)+9\left(2x-3\right)=0\)

\(\Leftrightarrow\left(2x-3\right)\left(x^2+12x+9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\x^2+12x+9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\\left(x+6\right)^2=27\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x+6=3\sqrt{3}\\x+6=-3\sqrt{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=3\sqrt{3}-6\\x=-3\sqrt{3}-6\end{matrix}\right.\)

Vậy: \(S=\left\{\dfrac{3}{2};3\sqrt{3}-6;-3\sqrt{3}-6\right\}\)

32,25 đúng nha bạn

\(21+\left(4,5.2,5\right)\)

\(=21+11,25\)

\(=32,25\)

=>\(\text{Cái thứ 2 đúng}\)

`-x-521=-17363`

`=>-x=-17363+521`

`=>-x=-16842`

`=>x=16842`

-x=-17363+521

-x=-16842

x=16842

x=16842

4,8 x(13,5-2,5) -1

4,8x (11-1)

4,8 x10

48

= 4,8 x 13,5 - 2,5 x 4,8 - 4,8 x 1

=    4,8 x (13,5 - 2,5 - 1)

=    4,8 x     10

=        48

Chúc bạn học tốt.

4,8 \(\times\) ( 13,5 - 2,5-1 ) 

= 4,8 \(\times\) 10

= 48

Tìm x

a) x - 1,27 = 13,5 : 4,5

x - 1,27 = 3

x = 1,27 + 3

x = 4,27

b) 8/3 - x = 2/5

x = 8/3 - 2/5

x = 34/15