Question

determinati cel mai mare numar natural n astfel incat: $1+ 2+ 2^{2} + 2^{3} +..........+ 2^{n} \leq 2050$

Answer 1

1,2,2²,2³....sunt termenii unei progresii geometrice care are primul termen 2⁰ si ratia 2
S=b1(qⁿ-1)/(q-1
b1=2⁰=1, q=2
1(2ⁿ-1)/(2-1)≤2050
2ⁿ≤2051=2048+3=2¹¹+3, n=11