Question

(2¹×2²×2³×...×2⁵⁰):(2¹⁷)⁷⁵​

Answer 1

Răspuns:

2¹⁰²⁰

Explicație pas cu pas:

(2¹×2²×2³×...×2⁵⁰):(2¹⁷)⁷⁵​ =

$= 2^{1+2+3+...+50} : 2^{17*15}$

Folosim formula pentru suma Gaus  $S_{n} = \frac{n(n+1)}{2}$

$= 2^{\frac{50*51}{2} } : 2^{255}$

$= 2^{1275} : 2^{255}$

$= 2^{1275-255}$

= 2​¹⁰²⁰