Toán 8 cần giải gấp!!

R

ronaldover7

Chắc đề là thế này
Chứng minh rằng $5^{2n+1}$ + $2^{n+4}$ + $2^{n+1}$ chia hết 23
Ta có:$5^{2n+1}$ + $2^{n+4}$ + $2^{n+1}$
=$5^{2n+1}+2^n(2^4+2)$
=$5^2{n+1}$+18.$2^n$
=$5^{2n+1}-5.2^n+23.2^n$
=$5(5^{2n}-2^n)+23.2^n$
=$5(25^n-2^n)+23.2^n=5.(25-2)(.......)+23.2^n$ chia hết 23​
 
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