I just need help with this.
Write the series in sigma notation.
1/4 + 1/2+ 3/4 + 1 + 5/4 + 3/2
5
A.) 1/4 sigma N
n=1
6
B.) 1/4 sigma n
n=1
5
C.)sigma n/n+3
n=1
6
D.)sigma n/n+3
n=1
using a denominator of 4, we have
14 + 2/4 + 3/4 + ... + 6/4 =
6
∑ n/4
n=1
looks like (B)
To write the series in sigma notation, we need to determine the pattern of the terms in the series.
The given series is: 1/4 + 1/2 + 3/4 + 1 + 5/4 + 3/2
By observing the sequence, we can see that the numerators of the fractions are increasing by 1 (1, 2, 3, 4, 5, 6) and the denominators are constant (4, 2, 4, 2, 4, 2).
In the sigma notation, the pattern becomes:
Σ(numerator/denominator)
where the numerator takes on the values 1, 2, 3, 4, 5, 6, and the denominator is constant at 4, 2, 4, 2, 4, 2.
Looking at the answer choices, only options C and D have a sigma notation format. Let's evaluate these options and choose the correct one.
C.) Σn/(n+3), n=1 from 5:
Plugging in n = 1 in the expression n/(n+3), we have 1/(1+3) = 1/4. However, this doesn't match the first term in the series.
D.) Σn/(n+3), n=1 from 6:
Plugging in n = 1 in the expression n/(n+3), we have 1/(1+3) = 1/4, which matches the first term in the series.
Now, let's evaluate the remaining terms by plugging in n = 2, 3, 4, 5, and 6 into the expression n/(n+3):
n = 2: 2/(2+3) = 2/5
n = 3: 3/(3+3) = 3/6 = 1/2
n = 4: 4/(4+3) = 4/7
n = 5: 5/(5+3) = 5/8
n = 6: 6/(6+3) = 6/9 = 2/3
Now, let's compare the terms we obtained with the given series: 1/4, 2/5, 1/2, 4/7, 5/8, 2/3
The terms we obtained match the terms in the given series. Therefore, option D is the correct answer:
D.) Σn/(n+3), n=1 from 6