Question

Use the formula to evaluate the series 1+2+4+8...+a10

Answer 1

Since this is a geometric series, let's use the sum to n terms of a geometric series given by:

$S_n = \frac{a(r^{n} - 1)}{r - 1}$, where a is the first term, r is the common ratio, and n is the number of terms.

We know that a = 1
Common ratio (r): 2
Num. of terms: 10

Plugging it all into the equation, we produce:
$S_{10} = \frac{1(2^{10} - 1)}{2 - 1}$
$= 2^{10} - 1$
$1,023$

Thus, the summation is 1,023