eumyang said:They aren't that massive. Rewrite them as fractions:
[tex]\frac{n^2(n+1)^2}{4}-\frac{n(n+1)(2n+1)}{6}[/tex]
Find a common denominator, rewrite both fractions so that both have that common denominator, and then subtract. It will be possible to factor things out.
Sigma Notation, also known as summation notation, is a mathematical notation used to represent the addition of a series of terms. It uses the Greek letter sigma (Σ) to indicate the sum, and a variable or expression below the sigma to represent the terms being added.
To use Sigma Notation to sum a series, you first write out the series in terms of the variable or expression below the sigma. Then, you replace the variable or expression with a starting value and an ending value, and the sigma indicates that you should add all the terms together. For example, the series 1 + 2 + 3 + 4 + 5 can be written as Σn from 1 to 5, where n is the variable representing each term.
The upper limit in Sigma Notation represents the last term in the series, while the lower limit represents the first term. For example, Σn from 1 to 5 means that you add all the terms from n=1 to n=5, so the upper limit is 5 and the lower limit is 1.
Yes, Sigma Notation can be used for both finite and infinite series. However, for infinite series, the notation is typically written as Σn from 1 to ∞, where ∞ represents infinity as the upper limit.
Some common properties of Sigma Notation include the ability to manipulate the limits, the ability to factor out constants, and the ability to add or subtract series with the same limits. It also follows the commutative and associative properties of addition, meaning that changing the order or grouping of terms will not affect the sum.