Question

(1+1+2+2²+2³+...+2 la puterea 100)•x=2 la puterea 101
Va rog ajutati.ma urgent!

Answer 1

Se stie ca
$2^1+2^2+2^3+...+2^n=2^{n+1}-2$
Atunci noi avem
$1+1+(2^1+2^2+...+2^{100})=2+2^{101}-2=2^{101}$
Ecuatia devine
$2^{101}\cdot x=2^{101} \\ x=1$

Answer 2

Valoarea parantezei se mai poate obtine ...
1+1  =2
2+2  =2²
2²+2²=2*2²=2³
2³+2³=2*2³=2⁴
........................
2¹⁰⁰+2¹⁰⁰=2*2¹⁰⁰=2¹⁰¹  
⇒ 2¹⁰¹ * x =2¹⁰¹ 
  x = 2¹⁰¹:2¹⁰¹ = 1