Question

Find the sum.
1+4+16...+65,536

Answer 1

its a gp series

Answer 2

since common ratio is same

Answer 3

whats the sum?

Answer 4

\[4^0 + 4^1+4^2 + \cdots + 4^8 \]

Answer 5

The r th term is:\[ax ^{r-1}\]
where a is the first term and x is the common ratio.
\[65536=4^{r-1}\]
Solving gives r = 9
So 65536 is the 9th term of the geometric progression
the sum of n terms is:\[\frac{a(x ^{n}-1)}{x-1}=\frac{4^{9}-1}{4-1}=87381\]

Answer 6

thank you!

Answer 7

You're welcome :)