Question

Afla numarul natural nenul N, stiind ca 2+ 2 la n + 2 la n+1 + 2 la n+2 + 2 la n+3 + 2 la n+4 + 2 la n+5 = 2018.

Answer 1

Răspuns:

5

Explicație pas cu pas:

2+2ⁿ+2ⁿ⁺¹+2ⁿ⁺²+2ⁿ⁺³+2ⁿ⁺⁴+2ⁿ⁺⁵=2018, => 2ⁿ+2ⁿ⁺¹+2ⁿ⁺²+2ⁿ⁺³+2ⁿ⁺⁴+2ⁿ⁺⁵=2018-2, => 2ⁿ+2ⁿ⁺¹+2ⁿ⁺²+2ⁿ⁺³+2ⁿ⁺⁴+2ⁿ⁺⁵=2016, => 2ⁿ·1 +2ⁿ·2¹+2ⁿ·2²+2ⁿ·2³+2ⁿ·2⁴+2ⁿ·2⁵=2016, => 2ⁿ·(1+2¹+2²+2³+2⁴+2⁵)=2016, =>  2ⁿ·(1+2+4+8+16+32)=2016, =>  2ⁿ·63=2016, => 2ⁿ=2016:63, => 2ⁿ=32, => n=5.