Write the series with summation notation
3+9+19+33+51+73
I'm not sure what the equation would be. Would this situation have two equations and if so how would that look like in summation notation
Sn = ∑[i=1..n]2i^2 + 1
To find the series with the given terms, we need to observe the pattern and find a general formula to generate the terms.
If we observe the given terms, we can see that the common difference between consecutive terms is increasing by 2 each time. Therefore, we can deduce that the formula for the nth term of the series is given by:
nth term = (n^2) + 2n + 1
Now, let's write the series using summation notation:
The series starts from n = 1, so we can re-write the given terms as follows:
3 = (1^2) + 2(1) + 1
9 = (2^2) + 2(2) + 1
19 = (3^2) + 2(3) + 1
33 = (4^2) + 2(4) + 1
51 = (5^2) + 2(5) + 1
73 = (6^2) + 2(6) + 1
Now, let's express the terms in summation notation:
The series can be written as:
∑[(n^2) + 2n + 1]
The summation is taken over the range of n = 1 to n = k, where k is the number of terms you want to sum.
Therefore, the series in summation notation is:
∑[(n^2) + 2n + 1] for n = 1 to k