Answer:
The sum of the given series is 1023
Step-by-step explanation:
Geometric series states that a series in which a constant ratio is obtained by multiplying the previous term.
Sum of the geometric series is given by:
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex]
where a is the first term and n is the number of term.
Given the series: [tex]1+2+4+8+.................+a_{10}[/tex]
This is a geometric series with common ratio(r) = 2
We have to find the sum of the series for 10th term.
⇒ n = 10 and a = 1
then;
[tex]S_n = \frac{1(1-2^{10})}{1-2} =\frac{1-1024}{-1} =\frac{-1023}{-1}=1023[/tex]
Therefore, the sum of the given series is 1023
