rewrite the series in sigma notation 4+16+64+...+256+1024

Answer 1

We note that the series is a geometric series with a common ratio of r=16/4=4
The first term, i=1, is given by
4=1*4^1=4^i
The second term, i=2, is given by
16=4^2=4^i
...
and the last term, i=5, is given by
1024=4^5=4^i

Therefore the summation is for
4^i for i=1 to i=5.

Answer 2

First, recognize that 4 + 16 + 64 + 256 + 1024 can be rewritten as:
4^1 + 4^2 + 4^3 + 4^4 + 4^5

Now, realize that this is just a sum of 4^n, where the lower limit of n is 1 and the upper limit is 5, as shown above.

Putting this into standard sigma notation yields:

5
Σ 4^n
n=1