Question

CMR: 3ⁿ⁺³ - 2.3ⁿ +2ⁿ⁺⁵ - 7.2ⁿ chia hết cho 25

Answer 1

ta có:

\(3^{n+3}-2.3^n+2^{n+5}-7.2^n=\left(3^{n+3}-2.3^n\right)+\left(2^{n+5}-7.2^n\right)\)

\(=3^n\left(3^3-2\right)+2^n\left(2^5-7\right)\)

\(=3^n\left(27-2\right)+2^n\left(32-7\right)\)

\(=3^n.25+2^n.25\)

\(=25\left(3^n+2^n\right)⋮25\)

vậy \(3^{n+3}-2.3^n+2^{n+5}-7.2^n⋮25\left(đpcm\right)\)

Answer 2

tách rồi nhân phân phối là đc

Answer 3

3^n.3^3-2.3^n+2^n.2^5-7.2^n=3^n(3^3-2)+2^n(2^5-7)chia hết cho 25