làm bài 2 câu 3,4 $5.12.0.11+7.(-2).27$,Bài 2: (4 điểm),1) Tìm số tự nhiên x, biết: $1600:[-41-(2x-5)^5]=(-2)^3.5$,2) Tìm $x\in N,$ biết: $2^x+2^{x+2}=\frac{200}{19}.(\frac1{1.2}+\frac1{2.3}+\frac1{3.4}+...+\frac1{19.20})$,3) Tìm x, biết: $\frac16+\frac1{12}+\frac1{20}+...+\frac1{x(x+1)}=\frac9{20}$,4) Tìm $x,y\in N,$ sao cho $2^x+624=5^y$

Question

làm bài 2 câu 3,4 $5.12.0.11+7.(-2).27$,Bài 2: (4 điểm),1)  Tìm số tự nhiên x, biết: $1600:[-41-(2x-5)^5]=(-2)^3.5$,2) Tìm $x\in N,$ biết: $2^x+2^{x+2}=\frac{200}{19}.(\frac1{1.2}+\frac1{2.3}+\frac1{3.4}+...+\frac1{19.20})$,3)  Tìm x,  biết: $\frac16+\frac1{12}+\frac1{20}+...+\frac1{x(x+1)}=\frac9{20}$,4) Tìm $x,y\in N,$ sao cho $2^x+624=5^y$

Accepted Answer

1,$\displaystyle 1600:\left[ -41-( 2x-5)^{5} ight] =( -2)^{3} .5$
$\displaystyle \begin{array}{{>{\displaystyle}l}}
\Rightarrow -41-( 2x-5)^{5} =1600:( -40) =-40\
\Rightarrow ( 2x-5)^{5} =-41+40=-1\
\Rightarrow 2x-5=-1\
\Rightarrow 2x=4\
\Rightarrow x=2
\end{array}$
2,$\displaystyle 2^{x} +2^{x+2} =\frac{200}{19} .\left(\frac{1}{1.2} +\frac{1}{2.3} +\frac{1}{3.4} +...+\frac{1}{19.20} ight)$
$\displaystyle \begin{array}{{>{\displaystyle}l}}
\Rightarrow 2^{x} +2^{x} .4=\frac{200}{19} .\left( 1-\frac{1}{2} +\frac{1}{2} -\frac{1}{3} +...+\frac{1}{19} -\frac{1}{20} ight)\
\Rightarrow 2^{x} .5=\frac{200}{19} .\left( 1-\frac{1}{20} ight)\
\Rightarrow 2^{x} =\frac{40}{19} .\frac{19}{20} =2\
\Rightarrow x=1
\end{array}$
3,$\displaystyle \frac{1}{6} +\frac{1}{12} +\frac{1}{20} +...+\frac{1}{x( x+1)} =\frac{9}{20}$
$\displaystyle \begin{array}{{>{\displaystyle}l}}
\Rightarrow \frac{1}{2.3} +\frac{1}{3.4} +\frac{1}{4.5} +...+\frac{1}{x( x+1)} =\frac{9}{20}\
\Rightarrow \frac{1}{2} -\frac{1}{3} +\frac{1}{3} -\frac{1}{4} +...+\frac{1}{x} -\frac{1}{x+1} =\frac{9}{20}\
\Rightarrow \frac{1}{2} -\frac{1}{x+1} =\frac{9}{20}\
\Rightarrow \frac{1}{x+1} =\frac{1}{2} -\frac{9}{20} =\frac{1}{20}\
\Rightarrow x+1=20\
\Rightarrow x=19
\end{array}$