Question

3. Demonstrați că (21.3n+1+2-6n+2):75.
VA ROG REPEDE
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Answer 1

Răspuns:

Explicație pas cu pas:

$2^n*3^{n+1} + 2*6^{n+2} =$

$=2^n*3^{n+1} + 2*[(3*2)^{n+2} ]=$

$=2^n*3^{n+1} + 2*(2)^{n+2}*(3)^{n+2} =$

$=2^n*3^{n+1} + 2^{n+3}*(3)^{n+2} =$

$=2^n*3^n*(3+ 2^3*3^2) =$

$=2^n*3^n*(3+ 8*9) =$

$=2^n*3^n*(3+ 72) =$

$=2^n*3^n*75 : 75$