Question

Efectuați: c) 4^15-3x4^14-3x4^13-...-3x4= d) 5^100-4x5^99-4x5^98-...-4x5​

Answer 1

Răspuns:

c) 4; d) 5

Explicație pas cu pas:

c)

${4}^{15} - 3 \cdot {4}^{14} - 3 \cdot {4}^{13} - ... - 3 \cdot 4 = {4}^{15} - 3 \cdot ({4}^{14} + {4}^{13} + ... + 4) = {4}^{15} - 3 \cdot \frac{4\cdot( {4}^{14} - 1)}{4 - 1} = {4}^{15} - 3 \cdot \frac{{4}^{15} - 4}{3} = {4}^{15} - {4}^{15} + 4 = \bf 4$

d)

${5}^{100} - 4 \cdot {5}^{99} - 4 \cdot {5}^{98} - ... - 4 \cdot 5 = {5}^{100} - 4 \cdot ({5}^{99} + {5}^{98} + ... + 5) = {5}^{100} - 4 \cdot \frac{5 \cdot ( {5}^{99} - 1)}{5 - 1} = {5}^{100} - 4 \cdot \frac{{5}^{100} - 5}{4} = {5}^{100} - {5}^{100} + 5 = \bf 5$