What is an nth partial sum?

What is an nth partial sum? What is an nth partial sum?

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Expert Solution

nth Partial Sum: The nth partial sum of a series is the sum of a finite number of consecutive terms beginning with the first term. The notation Sn is used to represent the partial sum.

For example: consider an arithmetic series,

2 + 5 + 8 + 11 + 14 + … + 32

The sum of first three terms of the above series will be represented by S3 and will be computed as follows:

S3 = 2 + 5 + 8

= 15

The sum of first six terms of the above series will be represented by S6 and will be computed as follows:

S6 = 2 + 5 + 8 + 11 + 14 + 17

= 57

Summation notation is used to represent series. It uses the Greek capital letter sigma to represent the sum. Summation notation includes an explicit formula and specifies the first and last term in the series.

For example consider the above arithmetic series. The explicit formula for the above arithmetic series is,

an = 2 + (k – 1)3

= 3k - 1

Last term 32 is the 11th term of the series. So, the above arithmetic series will be written as follows:

11Σk=1(3k – 1)

Umair answered 1 year ago

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