Question

URGENT! VĂ ROG! OFER COROANĂ+30 DE PUNCTE PRIMULUI RASPUNS CORECT!Scrieți ca o putere: (2 + 2 la puterea 2 + 2 la puterea 3 + ... + 2 la puterea 100 ) + 2

Answer 1

2+2^2+2^3+...+2^100+2=
|______________|-suma unei progresii geometrice cu 100 termeni,
ratia r=2,a1=2^1 .
Suma=a1*(r^n-1)/(r-1)
Suma=2*(2^100-1)/1
S=2*(2^100-1)
S=2^101-2
S+2=2^101-2+2=2^101
=> 2^1+2^2+.....+2^100+2=2^101

Answer 2

(2+2^2+2^3+...+2^100)+2=
=2+2+2^2+2^3+...+2^100=
=2^2+2^2+2^3+...+2^100=
=2^3+2^3+2^4+...+2^100=
=2^4+2^4+2^5+...+2^100=
..............................................
=2^100+2^100=2^101;
O formula valabila doar cand baza este 2:
2^x +2^x=2^(x+1)