Question

a, = a, = 2, a, = 0-1 2, a, = 0, -,-1, n > 2​

Answer 1

Answer:

Step-by-step explanation:

In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so in the usual sense it has no sum. In a much broader sense, the series is associated with another value besides ∞, namely −1, which is the limit of the series using the 2-adic metric.

The partial sums of {\displaystyle 1+2+4+8+\cdots }{\displaystyle 1+2+4+8+\cdots } are {\displaystyle 1,3,7,15,\ldots ;}{\displaystyle 1,3,7,15,\ldots ;} since these diverge to infinity, so does the series.

{\displaystyle 2^{0}+2^{1}+\cdots +2^{k}=2^{k+1}-1}{\displaystyle 2^{0}+2^{1}+\cdots +2^{k}=2^{k+1}-1}