Question

pls ajutati ma cat mai repedeee(c si d)

Answer 1

Răspuns:

c) 4; d) 5

Explicație pas cu pas:

c)

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

sau

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

$= {4}^{14} \cdot (4 - 3) - 3 \cdot {4}^{13} - ... - 3 \cdot 4$

$= {4}^{14} - 3 \cdot {4}^{13} - ... - 3 \cdot 4$

$= {4}^{13} \cdot (4 - 3) - 3 \cdot {4}^{13} - ... - 3 \cdot 4$

$= {4}^{13} - 3 \cdot {4}^{13} - ... - 3 \cdot 4 = ...$

$= {4}^{2} - 3 \cdot 4 = 4 \cdot (4 - 3) = \bf 4$

d)

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

sau

${5}^{100} - 4 \cdot {5}^{99} - 4 \cdot {5}^{98} - ... - 4 \cdot 5 =$

$= {5}^{99} \cdot (5 - 4) - 4 \cdot {5}^{98} - ... - 4 \cdot 5$

$= {5}^{99} - 4 \cdot {5}^{98} - ... - 4 \cdot 5$

$= {5}^{98} \cdot (5 - 1) - ... - 4 \cdot 5$

$= {5}^{98} - ... - 4 \cdot 5 = ...$

$= {5}^{2} - 4 \cdot 5 = 5 \cdot (5 - 4) = \bf 5$