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1) \(+2x+3y⋮17\)
\(\Rightarrow26x+39y⋮17\)
\(\Rightarrow\left(9x+5y\right)+17x+34y⋮17\)
Mà \(17x+34y⋮17\)
\(\Rightarrow9x+5y⋮17\)
\(+9x+5y⋮17\)
\(\Rightarrow36x+20y⋮17\)
\(\Rightarrow\left(2x+3y\right)+34x+17y⋮17\)
Mà \(34x+17y⋮17\)
\(\Rightarrow2x+3y⋮17\)
A=( 4^5/4+4^5/4^2+4^5/4^3+4^5/4^4 )+.....................+ ( 4^101/4^97+....+4^101/4^100 )
A = ( 4^4+ 4^3+4^2+4 ) + .........................................+ ( 4^4 + 4^3+4^2+4)
A= ( 4^4 + 4^ 3+ 4^2+4 ) * ( (101-5):4+1)
A = (4^4+4^3+4^2+4) * 25
A =( 256+81+16+4)*25= 8925
k cho mình nhé
câu g)
\(G=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{121}-1\right).\)
\(=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}...\cdot\frac{120}{121}\)
\(=\frac{3.\left(2.4\right).\left(3.5\right)...\left(10.12\right)}{2.2.3.3.4.4.5.5....11.11}\)
\(=\frac{12}{3}=4\)
\(B=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{99}{1}+\frac{98}{2}+\frac{97}{3}+...+\frac{1}{99}}\)
\(B=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\left(\frac{98}{2}+1\right)+\left(\frac{97}{3}+1\right)+...+\left(\frac{1}{99}+1\right)+1}\)
\(B=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{100}{2}+\frac{100}{3}+...+\frac{100}{99}+\frac{100}{100}}\)
\(B=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}+\frac{1}{100}\right)}\)
\(B=\frac{1}{100}\)
CMR: A<0,1
Ta có : \(A=\frac{1}{3^2}-\frac{1}{3^4}+\frac{1}{3^6}-\frac{1}{3^8}+....+\frac{1}{3^{98}}-\frac{1}{3^{100}}\)(1)
=> 32.A = \(1-\frac{1}{3^2}+\frac{1}{3^4}-\frac{1}{3^8}+...+\frac{1}{3^{96}}-\frac{1}{3^{98}}\)(2)
Lấy (2) cộng (1) theo vế ta có :
32.A + A = \(\left(\frac{1}{3^2}-\frac{1}{3^4}+\frac{1}{3^6}-\frac{1}{3^8}+...+\frac{1}{3^{98}}-\frac{1}{3^{100}}\right)+\left(1-\frac{1}{3^2}+\frac{1}{3^4}-\frac{1}{3^6}+...+\frac{1}{3^{96}}-\frac{1}{3^{98}}\right)\)
10A = \(1-\frac{1}{3^{100}}\)
=> A = \(\left(1-\frac{1}{3^{100}}\right):10=\frac{1}{10}-\frac{1}{3^{100}.10}=0,1-\frac{1}{3^{100}.10}< 0,1\)
=> A < 0,1 (ĐPCM)