Help please!
Write the series in sigma notation.
1/4+1/2+3/4+1+5/4+3/2
rewrite as
1/4 + 2/4 + 3/4 + 5/4 + 6/4
so the general form of the terms are n/4
∑ n/4 , where n=1 to 4
write the "n=1" below the ∑ sign, and 4 above it
Hello Reiny,
Thanks for the help however it's a multiple choice and ther is non like that.
I have:
A. 1/4 to the left of the e symbol. 5 on top n=1 on the bottom and n to the right.
b. 1/4 to the left, 6 on top, n to the right and n=1 on the bottom.
c. 5 on the top, n=1 on the bottom and to the right n/n+3
d. 6 on the top. n=1 on the bottom and to the right n/n+3.
I obviously can't count to 5, only saw 4 terms, ha ha
you should have seen that
how about
∑ n/4 , where n=1 to 5
= (1/4) ∑ n , where n=1 to 5
To write the series in sigma notation, we need to find a pattern that relates the terms. In this case, the pattern seems to be that each term is obtained by adding 1/4, 1/2, 3/4, 1, and so on, to the previous term.
Let's break down the terms in the series to understand the pattern better:
1/4 + 1/2 + 3/4 + 1 + 5/4 + 3/2
If we observe, we notice that the numerator of each term is obtained by adding 1 to the previous term's numerator, and the denominator is always 2.
To create the sigma notation, we first need to determine the starting point, the ending point, and the expression of the terms in the series.
Starting from the first term (1/4), we can see that each subsequent term is obtained by adding 1/4 to the previous fraction. We can also observe that the denominators are constant at 2.
Let's set up the sigma notation for the series:
∑(k=0 to n) [(1 + k/4) / 2]
In this notation:
- The sigma (∑) indicates the sum of the terms.
- 'k' is the variable representing the index.
- '0' is the starting point of the series.
- 'n' is the ending point or the last term we want to include.
Now, if you want to write the series up to a specific term, let's say the 6th term, we replace 'n' with 5:
∑(k = 0 to 5) [(1 + k/4) / 2]
This notation represents the sum of the series from the first term to the 6th term. To find the sum, you can simplify the expression and evaluate it.
Keep in mind that sigma notation represents the sum of a series. If you want to find the sum of the series, you need to evaluate the expression within the sigma notation.