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
[tex]\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}}[/tex]
