Question

What is the sum of the geometric series
2^0+2^1+2^2+2^3+2^4+...+2^9 ?

Answer 1

there is an easy enough formula for this
do you know it?

Answer 2

it is even easier with powers of two than with other powers \[2^0+2^1+2^2+...+2^n=2^{n+1}-1\]

Answer 3

you can divide \(\large\color{#000000 }{ \displaystyle r^{n+1}-1 }\) by \(\large\color{#000000 }{ \displaystyle r-1 }\) and you will the series

Answer 4

Thank you😁

Answer 5

For example

\(\large\color{#000000 }{ \displaystyle 1+r+r^2+r^3+r^4=(r^{5}-1)/(r-1) }\)