Question

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

Answer 1

`1023`

Explanation:

The formula is

`S_n = \frac{a(1 - {r}^(n)) }{1 - r}`

The given series is:

`1 + 2 + 4 + 8 + ... + a_(10)`

where the first term is a=1 and the common ratio is

`r = (2)/(1) = 2`

We plug in all these values to get:

`S_(10) = \frac{1(1 - {2}^(10)) }{1 - 2}`

`S_(10) = (1 - 1024)/( - 1) = 1023`