Question

a) 3+3putere2 + 3putere 3 +.....+ 3putere 48

b) 2+ 2putere2 + 2putere 3 +.....+ 2putere 51

c) 5+5putere2+5putere3+.....+ 5putere81

d)1+7+7putere2+ ....... + 7putere 102





VA ROG

Answer 1

$\text{Iti arat cum se rezolva prima(restul sunt asemanatoare):}\\a)\text{Notam suma cu S}:\\S=3+3^2+3^3+\ldots+3^{48} \\\text{Inmultind aceasta suma cu S se obtine:}\\3S=3^2+3^3+3^4+\ldots+3^{49}\\\text{Scadem S din 3S:}\\3S-S=3^{49}-3\\2S=3^{49}-3\\\boxed{S=\dfrac{3^{49}-3}{2}}$