Exam Questions - Sum of series

Sum of Series

A series refers to the sum of the terms of a sequence.
It can either be a finite series, where there’s a distinct number of terms, or an infinite series, which has infinite terms.
Series can further be classified as arithmetic, where each term differs from the next by a constant difference, or geometric, where each term is a fixed multiple of the previous term.

The sum of an arithmetic series can be found using the formula S = n/2 ( 2a + (n-1)d ), where ‘S’ is the sum of the series, ‘n’ is the number of terms, ‘a’ is the first term and ‘d’ is the common difference.
When applying this formula, make sure you have correctly identified the first term (a), the common difference (d) and the number of terms (n).

To find the sum of a finite geometric series, the formula S = a ( 1 - r^n ) / ( 1 - r ) is used. Here, ‘S’ is the sum of the series, ‘a’ is the first term, ‘r’ is the common ratio, and ‘n’ is the number of terms.
For infinite geometric series with a common ratio ‘r’ whose absolute value is less than 1, the sum can be calculated by S = a / ( 1 - r ).
Accurately identifying the first term (a), the common ratio (r), and the number of terms (n) is essential when using these formulae.

Pay close attention to the details given in the question to clearly identify whether the series is arithmetic or geometric.
Determine the first term, common difference/ratio and number of terms correctly before using the relevant formula.
For infinite geometric series, ensure that the absolute value of r is less than 1 to ascertain whether the series actually verges on a sum.
Get plenty of practice in applying these formulae to varied problems to establish confidence and competency in this area.
Reread your answers and check your calculations, as errors can easily creep into series sum problems, particularly with complicated geometrical series.
Remember that patience and practice will greatly enhance your understanding and precision when working on series sum problems.