C/m nó nhỏ hơn ³/₄ hả bạn ?

Có \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}< \frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

                                                      \(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

                                                        \(=\frac{1}{4}+\frac{1}{2}-\frac{1}{100}< \frac{3}{4}\)

ĐKXĐ: \(x\notin\left\{0;-9\right\}\)

Ta có: \(\dfrac{1}{x+9}-\dfrac{1}{x}=\dfrac{1}{5}+\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{20x}{20x\left(x+9\right)}-\dfrac{20\left(x+9\right)}{20x\left(x+9\right)}=\dfrac{4x\left(x+9\right)+5x\left(x+9\right)}{20x\left(x+9\right)}\)

Suy ra: \(4x^2+36x+5x^2+45x=20x-20x-180\)

\(\Leftrightarrow9x^2+81x+180=0\)

\(\Leftrightarrow x^2+9x+20=0\)

\(\Leftrightarrow x^2+4x+5x+20=0\)

\(\Leftrightarrow x\left(x+4\right)+5\left(x+4\right)=0\)

\(\Leftrightarrow\left(x+4\right)\left(x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\left(nhận\right)\\x=-5\left(nhận\right)\end{matrix}\right.\)

Vậy: S={-4;-5}

A=1/4(1/1+1/2^2+...+1/50^2)

=>A=1/4+1/4*(1/2^2+...+1/50^2)

=>A<1/4+1/4*(1-1/2+1/2-1/3+...+1/49-1/50)

=>A<1/4+1/4*49/50=99/200<1/2

1)Tính:

a)\(4^2\cdot2=\left(2^2\right)^2\cdot2=2^4\cdot2=2^5=32\)

b)\(36^2:6^2=\left(36:6\right)^2=6^2=48\)

c)\(\left(\frac{2}{5}\right)^{10}:\left(\frac{4}{25}\right)^2=\left(\frac{2}{5}\right)^{10}\cdot\left(\frac{25}{4}\right)^2=\)\(\left(1\right)^{10}\cdot\left(\frac{5}{2}\right)^2=1\cdot\frac{5^2}{2^2}=1\cdot\frac{25}{4}=\frac{25}{4}\)

a

\(4^2.2=16.2=32\)

b\(36^2:6^2=36.36:6.6=36.36:36=36\)

c

3)

a)\(x:\left(-\frac{1}{3}\right)^5=\left(-\frac{1}{3}\right)^3\)

                      \(x=\left(-\frac{1}{3}\right)^3\cdot\left(-\frac{1}{3}\right)^5\)           

                      \(x=\left(-\frac{1}{3}\right)^8\)

b)\(\left(\frac{2}{3}\right)^{16}\cdot x=\left(\frac{2}{3}\right)^{18}\)

                      \(x=\left(\frac{2}{3}\right)^{18}:\left(\frac{2}{3}\right)^{16}\)

                      \(x=\left(\frac{2}{3}\right)^2\)

                      \(x=\frac{2^2}{3^2}\)

                      \(x=\frac{4}{9}\)

yêu cầu đề bài là gì đây ạ?? Tính hay là CM??

Chứng minh cái gì hả bạn?