Question

Which represents the sum of the geometric series: 6 + 12 + 24 + 48 + … + 12,288?

Answer 1

if we divide it all by 6 we might be able to see our common ratio

Answer 2

ok so this is a "geometric" series, do you see to get the next term we add 2 times the last?

Answer 3

add 6

Answer 4

or divide \(\frac{a_n}{a_{n-1}}\)

Answer 5

\(6\times (1+2+2^2+2^3+...+2^{11})\)

Answer 6

so you get
\[6\times (2^{12}-1)\] whatever that is

Answer 7

i always remember 2^10 = 1024

Answer 8

\[6\times(2^{12} -1) = 6(1024\times4 -1)\]