Question

C=4¹⁵-3*4¹⁴- 3*4¹³-...-3*4 = ​

Answer 1

Explicație pas cu pas:

$C = {4}^{15} - 3 \times {4}^{14} - {4}^{13} - ... - 3 \times 4$

$= {4}^{15} - 3 \times({4}^{14} + {4}^{13} + ... + 4)$

(suma unei progresii geometrice, cu primul termen 4, rația 4, 14 termeni)

$= {4}^{15} - 3 \times \frac{4 \times {4}^{14 - 1} }{4 - 1} = {4}^{15} - 3 \times \frac{ {4}^{14} }{3}$

$= {4}^{15} - {4}^{14} = {4}^{14}(4 - 1)$

$= 3 \times {4}^{14}$