Question

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Answer 1

Răspuns:

Explicație pas cu pas:

2^32 - 2^30 - 2^28 - 2^26 = 2^26*(2^6 - 2^4 - 2^2 - 1)

= 2^26*(64 - 16 - 4 - 1) = 43*2^26

4^17 - 4^16 - 4^15 - 4^14 = 4^14*(4^3 - 4^2 - 4 - 1)

= 4^14*(64 - 16 - 4 - 1) = 43*4^14 = 43*(2^2)^14 = 43*2^28

fractia devine

43*2^26/43*2^28 = 1/2^2 = 1/4

____________________

7^n + 7^(n+1) + 7^(n+2) = 7^n*(1 + 7 + 7^2) = 57*7^n

2^n + 2^(n+1) + 2^(n+4) = 2^n*(1 + 2 + 2^4) = 19*2^n

fractia devine

57*7^n/19*2^n = 3*7^n/2^n

Answer 2

Răspuns:

a) 2³²-2³⁰-2²⁸-2²⁶=2²⁶(2⁶-2⁴-2²-1)=2²⁶(64-16-4-1)=2²⁶·43

4¹⁷-4¹⁶-4¹⁵-4¹⁴=4¹⁴(4³-4²-4-1)=4¹⁴(64-16-4-1)=(2²)¹⁴·43=2²⁸·43

(2²⁶·43)/(2²⁸·43)=1/2²=1/4

b) 7ⁿ+7ⁿ⁺¹+7ⁿ⁺²=7ⁿ(1+7+7²)=7ⁿ(1+7+49)=7ⁿ·57

2ⁿ+2ⁿ⁺¹+2ⁿ⁺⁴=2ⁿ(1+2+2⁴)=2ⁿ(1+2+16)=2ⁿ·19

(7ⁿ·57)/(2ⁿ·19)=(3·7ⁿ)/2ⁿ

Explicație pas cu pas: