Write the series as a summation in sigma notation

6 + 12 + 24 + 48

3

∑ 6*2^k
k=0

or

4
∑ 3*2^k
k=1

The series 6 + 12 + 24 + 48 can be written in sigma notation as:

∑(n=1 to 4) 6 * 2^(n-1)

In this notation, the term 'n' represents the index of summation, starting from 1 and going up to 4 in this case. The expression '6 * 2^(n-1)' represents the general term of the series, where each term is found by multiplying 6 by 2 raised to the power of (n-1).

To write the series as a summation in sigma notation, we need to determine the pattern or rule that generates each term in the series.

Looking at the series, we notice that each term is obtained by multiplying the previous term by 2. So, the pattern can be described as follows:

First term (n = 1) = 6
Second term (n = 2) = 6 * 2 = 12
Third term (n = 3) = 12 * 2 = 24
Fourth term (n = 4) = 24 * 2 = 48

We can express the general term of the series as 6 * 2^(n-1), where n is the position of the term in the series.

Now, let's write the series as a summation using sigma notation:

∑(n=1 to 4) 6 * 2^(n-1)

In this notation, the variable n represents the position of each term in the series. The lower limit of the summation is 1, and the upper limit is 4. The expression after the sigma symbol (∑) describes the general term of the series, which is 6 * 2^(n-1).

Therefore, the series 6 + 12 + 24 + 48 can be written in sigma notation as ∑(n=1 to 4) 6 * 2^(n-1).