How do you write the summation notation for:
1.) 4 - 24 + 144 - 864 + ... ?
2.) summation notation for: 729 + 1000 + 1331 + 1728 + ... + n^3
Sigma notation is a mathematical notation used to represent sums of a sequence of numbers. It is represented by the Greek letter sigma (Σ) and the numbers being summed are written below and above the sigma symbol. For example, Σn=1^5 n would represent the sum of all numbers from 1 to 5 (1+2+3+4+5=15).
Sigma notation is read as "the sum of" followed by the expression being summed. For example, the notation Σn=1^5 n would be read as "the sum of n from 1 to 5" or "the sum of n as n goes from 1 to 5".
The lower limit in sigma notation represents the starting point of the sequence being summed, while the upper limit represents the ending point. The numbers between the limits are the terms being summed. For example, in the notation Σn=1^5 n, the lower limit is 1 and the upper limit is 5.
To evaluate a sigma notation expression, you need to substitute the upper limit and lower limit values into the expression and perform the indicated operations. For example, in the notation Σn=1^5 n, the expression is n and the upper and lower limits are 1 and 5 respectively. Substituting these values, we get 1+2+3+4+5=15.
Sigma notation is commonly used in mathematics and science to represent sums of sequences or series. It is also used in statistics to represent the mean or average of a set of numbers. Additionally, it is used in calculus to represent integrals and in physics to represent summation of forces or work done.