Express the um using sigma notation:
1 +3/4 +5/9+ 7/16+ 9/25
what, you don't recognize
1,3,5,7,9,...
1,4,9,16,25,...
??
∑ (2k-1)/k^2
maybe
a(1) = 1
a(n+1) = (a(n)+2)/n^2
sum = sigma from n=1 to n = 5 of a(n)
oobleck gave better answer.
Thank you very much :)
What oobleck said, but with the upper and lower limits will give:
n=5
∑ (2k-1)/k^2
n=1
To express the given series using sigma notation, you can use the following steps:
Step 1: Find the general form of each term in the series.
Looking at the given series, you can observe that the numerator of each term is just the odd integers (starting from 1) while the denominator is the square of these odd integers. Therefore, the general form of each term can be written as (2n - 1) / (n^2), where n represents the position of the term.
Step 2: Determine the limits of the series.
Looking at the given series, you can see that the terms go up to the 5th term. Hence, the limits of the series can be denoted as n = 1 to 5.
Step 3: Write the series using sigma notation.
Now, by combining the general form of the terms and the limits, you can express the series in sigma notation as follows:
∑[(2n - 1) / (n^2)] from n = 1 to 5.
In this notation, the capital sigma (∑) represents the sum and the expression inside the parentheses represents the general form of each term, with the limits of the series specified below and above the sigma symbol respectively.