Answer:
Sum = 1,023
Step-by-step explanation:
The given series is:
1 + 2 + 4 + 8 + ........ + a₁₀
The given series is a geometric series.
It is required to find the sum of the first 10 terms
The sum to n terms of a geometric series given by: [tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex]
Where: a = the first term = 1
r = common ratio = 2/1 = 2
n = number of terms = 10
So,
[tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex] = [tex]\frac{1*(2^{10} -1)}{2-1} = 2^{10} -1 = 1024 - 1 = 1,023[/tex]
So, the summation of the series = 1,023
