Question

Daca 1 + 2+2²+2³+...+2⁵⁰=2 la puterea n -1, determinați numărul natural n ​

Answer 1

Răspuns:

1+x+x²+x³+...+xⁿ = xⁿ⁺¹ -1/ x-1

in cazul nostru, S=  2ⁿ⁺¹-1/2-1, unde n=50 ( din formula!!!!)

deci 2⁵⁰⁺¹-1=2ⁿ⁻¹ <=> log₂ (2⁵¹-1)= log₂ 2ⁿ⁻¹

<=> n-1= log₂ (2⁵¹-1)

<=> n= log₂ (2⁵¹-1) +1

<=> n= log₂ (2⁵¹-1) +1

<=> n≅52