Question

Să se calculeze a = 4+ 3·4 +3·4² + 3.4³ +...+3.4 la puterea 2010​

Answer 1

Explicație pas cu pas:

$a = 4 + 3\cdot {4}^{1} + 3\cdot {4}^{2} + 3\cdot {4}^{3} + ... + 3\cdot {4}^{2010} =$

$= 4 + 3\cdot({4}^{1} + {4}^{2} + {4}^{3} + ... + {4}^{2010}) =$

$= 4 + 3\cdot \frac{4\cdot( {4}^{2010} - 1)}{4 - 1} =$

$= 4 + 3\cdot \frac{( {4}^{2011} - 4)}{3} =$

$= 4 + {4}^{2011} - 4$

$= \bf {4}^{2011}$