Question

a/ 10ⁿ⁺¹ - 6.10ⁿ

B/ 2ⁿ⁺³ + 2ⁿ⁺² - 2ⁿ⁺¹ +2ⁿ

C/ 90.10^k - 10^{k +2} + 10^k +1

D/ 2,5 . 5^n-3 . 10+5ⁿ -6 .5^n-1

Answer 1

\(a, 10^{n+1} -6.10 ^n\)

= \(10^n (10-6)=4.10^n\)

\(B/ 2^{n+3} + 2^{n+2} - 2^{n+1} +2^n\)

= \(2^n (2^3+2^2-2+1)\)

= \(2^n (8+4-2+1)\)

\(= 11.2^n\)

\(C/ 90.10^k - 10^{k +2} + 10^{k +1} \)

\(= 10^k(90-2+1)\)

= \(89.10^k\)

\(D/ 2,5 . 5^{n-3} . 10+5^n -6 .5^{n-1}\)

\(= 5.5.5^{n-3} +5^n-6.5^{n-1}\)

= \(5^2 .5^{n-3}+5^n-6.5^{n-1} \)

= \(5^{n-3+2}+5^n -6.5^{n-1}\)

\(= 5^{n-1}(1+5-6)\)

= \(5^{n-1}.0\)

= 0