Question

Calculati suma

1+2+4+8+16+.....$2 ^{n+1}$ =

Answer 1

Răspuns:

x = 2ⁿ⁺² - 1

Explicație pas cu pas:

x = 1+2+4+8+16+.........+2ⁿ⁺¹ = >

x = 2⁰+2¹+2²+2³+........+2ⁿ⁺¹   I ·2 =>

2x = 2¹+2²+2³+2⁴+......+2ⁿ⁺¹ + 2ⁿ⁺² =>

2x = x-1 +2ⁿ⁺² =>

x = 2ⁿ⁺² - 1

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