Question

Fie suma a=2^0+2^1+2^2+....+2^2014.Scrie sub forma de putere a lui 2 suma a+1

Answer 1

a = 2⁰+2¹+2²+....+2²⁰¹⁴

2a = 2¹+2²+....+2²⁰¹⁴+2²⁰¹⁵

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2a - a = 2²⁰¹⁵ - 2⁰

a = 2²⁰¹⁵ - 1

⇒ a + 1 = 2²⁰¹⁵ - 1 + 1 = 2²⁰¹⁵

Answer 2

 

$\displaystyle\\a=2^0+2^1+2^2+\ldots+2^{2014}=\frac{2^{2014+1}}{2-1}-1=\frac{2^{2015}}{1}-1=2^{2015}-1\\\\\boxed{\bf~a=2^{2015}-1}\\\\a+1=(2^{2015}-1)+1=2^{2015}-1+1=2^{2015}\\\\\boxed{\bf~a+1=2^{2015}}$