Blog Option 2
Explain how you know what kind of sequence/series this is.
You can tell that this is a geometric series by either looking at the equation and seeing that r finds itself as an exponent or by testing three values and seeing the pattern of the difference between them, where one will observe that every value is the product of the previous value multiplied by 2.
Explain how you know what kind of sequence/series this is.
You can tell that this is a geometric series by either looking at the equation and seeing that r finds itself as an exponent or by testing three values and seeing the pattern of the difference between them, where one will observe that every value is the product of the previous value multiplied by 2.
Explain what each element of the summation notation is.
- The 7 above sigma represents the position of the final term in the series (stopping point/upper limit of the summation).
- The r below sigma is the index for the summation (the variable in the equation to the right to which the position of a term will be placed so that its value be obtained).
- The 4 below sigma represents the position of the first term in the series (starting point/lower limit of the summation).
- The expression to the right is known as the 'typical element' and is used to determine the value for a term by replacing the variable for the term's position.
Explain how to do this expansion of 4 terms.
Starting with 4 (lower limit of summation), replace the variable in the expression to the right of sigma by the value and calculate the result. Do this for the remaining whole numbers up to 7 (upper limit of summation). By placing the four terms side by side, as seen below, they have been expanded. To complete the summation, simply add all four terms.
Starting with 4 (lower limit of summation), replace the variable in the expression to the right of sigma by the value and calculate the result. Do this for the remaining whole numbers up to 7 (upper limit of summation). By placing the four terms side by side, as seen below, they have been expanded. To complete the summation, simply add all four terms.
- 16 + 32 + 64 + 128 = 240