Question

comparați numerele : a=
$1 + 2 ^{0} + 2 {}^{1} + 2 {}^{2} + .........2 {}^{98}$
b=
$3 {}^{66}$
​

Answer 1

Folosind formula

$2 {}^{0} + {2}^{1} + 2 {}^{2} + ... + 2 {}^{n} = 2 {}^{n + 1} - 1$

a=2⁹⁹-1

Aducem la un exponent comun:

2⁹⁹=(2³)³³=8³³

b=3⁶⁶=(3²)³³=9³³

Comparam:

a=8³³-1

b=9³³

Cum 8<9|⇒a<b

(n-1)<n |