A = 1/2 + 1/6 + 1/12 + .. + 1/6480

A= 1/1 x 2 + 1/2 x 3 + 1/3 x 4 + ... + 1/80 x 81

A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/80 - 1/81

A = 1 - 1/81

A = 80/81

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{6480}\)

\(A=\frac{1}{1}\times2+\frac{1}{2}\times3+\frac{1}{3}\times4+...+\frac{1}{80}\times81\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{80}-\frac{1}{81}\)

\(A=1-\frac{1}{81}\)

\(A=\frac{80}{81}\)

\(\left(2x-1\right)^6=\left(2x-1\right)^8.\)

\(\Leftrightarrow\left(2x-1\right)^8-\left(2x-1\right)^8=0\)

\(\Leftrightarrow\left(2x-1\right)^6.\left[\left(2x-1\right)^2-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(2x-1\right)^6=0\\\left(2x-1\right)^2-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x-1=0\\\left(2x-1\right)^2=1\end{cases}}\)

Đến đây bạn tự giải nha.

x=1/2 hoặc x=1 hoặc x=0

\(\Rightarrow\orbr{\begin{cases}2x=1\\\orbr{\begin{cases}\\2x-1=-1\end{cases}}2x-1=1\end{cases}}\)

suy ra 2x -1=0

2x=1

x=1:2

x=\(\frac{1}{2}\)

Ta có: 12⁴⁵=12^3.15=1728¹⁵

Vì 625¹⁵<1728¹⁵ nên 625¹⁵<12⁴⁵

Ta có: 12⁴⁵=12^3.15=1728¹⁵

Vì 625¹⁵<1728¹⁵ nên 625¹⁵<12⁴⁵

a)\(\frac{a}{b}< \frac{c}{d}\Rightarrow\frac{a}{b}.bd< \frac{c}{d}.bd\Rightarrow ad< cb\)(đpcm)

b)Ta có: 

• ad<cd

=>ab+ad<ab+cd

=>a(b+d)<b(b+d)

=>\(\frac{a\left(b+d\right)}{b\left(b+d\right)}< \frac{b\left(a+c\right)}{b\left(b+d\right)}\)

=>\(\frac{a}{b}< \frac{a+c}{b+d}\)(1)

•  ad<bc

=>ad+cd<bc+cd

=>d(a+c)<c(b+d)

=>\(\frac{d\left(a+c\right)}{d\left(b+d\right)}< \frac{c\left(b+d\right)}{d\left(b+d\right)}\)

=>\(\frac{a+c}{b+d}< \frac{c}{d}\)(2)

Từ (1) và (2) => \(\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}\)(đpcm)

a)(-7 / 5 + 3 / 8 ) : 2009 / 2010 + (-3 / 5+5 / 8) : 2009 / 2010

=[ (-7 / 5 + 3 / 8 ) + (-3 / 5+5 / 8) ] : 2009/2010

=[ -7/5 +3/8 + (-3)/5+5/8 ] : 2009/2010

=[ (-7/5 + (-3)/5) + (3/8 + 5/8) ] :2009/2010

=[-2+1] : 2009/2010

=-1 :2009/2010

=-2009/2010

b)\(\frac{9^8\cdot4^3}{27^4\cdot6^5}=\frac{\left(3^2\right)^8\cdot\left(2^2\right)^3}{\left(3^3\right)^4\cdot\left(2\cdot3\right)^5}=\frac{3^{16}\cdot2^6}{3^{12}\cdot2^5\cdot3^5}=\frac{3^{16}\cdot2^5\cdot2}{3^{16}\cdot3^1\cdot2^5}=\frac{2}{3^1}=\frac{2}{3}\)

123654321

123654321

cach giai

goi a la so can tim ta co

a chia het cho 2,3,4,5,6 suy ra cstc la 0

tiep theo a chia het cho 7,8,9 suy ra 

mk hết bít xin lỗi bn