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2+4+8+…+2n=2046
Cu formula va rog


Răspuns :

2+4+8+.....+2ⁿ = 2046 <=>

2¹+2²+2³+.....+2ⁿ = 2046 =>

a = 2¹+2²+2³+.....+2ⁿ   I·2

2a = 2²+2³+2⁴+.....+2ⁿ+2ⁿ⁺¹ = 2ⁿ⁺¹-2 +a

a = 2(2ⁿ-1) = 2046

2ⁿ-1 = 1023

2ⁿ = 1024

2ⁿ = 2¹⁰  => n = 10