Question

Calculeaza 2*(1+3+3 la puterea 2+...+3 la puterea 49)
Urgeeeeeeeent va rog

Answer 1

S=1+3+3²+...+3⁴⁹        inmultim cu 3
3S=3+3²+3³...+3⁴⁹+3⁵⁰
scadem S
3S-S=3+3²+3³...+3⁴⁹+3⁵⁰-(1+3+3²+...+3⁴⁹)
2S=3⁵⁰-1
S=(3⁵⁰-1)/2

2*(1+3+3²+...+3⁴⁹)=2*(3⁵⁰-1)/2=3⁵⁰-1

Answer 2

$2*(1+3+3^{2}+...+3^{49})$

[tex]Notez~cu~S=1+3+3^{2}+...+3^{49} Inmultind~relatia~cu~3~obtin: 3S=3+3^{2}+...+3^{50} 3S-S=3+3^{2}+...3^{50}-1-3-...-3^{49} 2S=3^{50}-1[/tex] [tex]S= \frac{3^{50}-1}{2} [/tex] [tex]2* \frac{3^{50}-1}{2} =3^{50}-1 [/tex]