How To Find The Sum Of An Infinite Geometric Series

The formula for the sum of an infinite series is related to the formula for the sum of the first.

How to find the sum of an infinite geometric series. In the case of the geometric series you just need to specify the first term a and the constant ratio r. In this case multiplying the previous termin the sequenceby 1313gives the next term. S n a 1 1 r n 1 r. When the sum of an infinite geometric series exists we can calculate the sum.

Plug in and simplify to find the following. You can use sigma notation to represent an infinite series. 1 49 343 select the correct choice below and if necessary fill in the answer boxes to complete your choice. Displaystyle s nfrac a 1left 1 r nright 1 r s.

Link to next video. Calculate a2 by plugging in 2 for n. Plug a1 and r into the formula to find the infinite sum. See in a later chapter how we use the sum of an infinite gp and differentiation to find polynomial approximations for functions.

We also see how a calculator works using these progressions. This video is a part of mathematics for economics iii. To find the sum of an infinite geometric series having ratios with an absolute value less than one use the formula s a1 1 r where a1 is the first term and r is the common ratio. Repeating decimals also can be expressed as infinite sums.

Consider the number 05555555. It is a course offered to the students studying for the third semester ba economics course in the university of kerala. For example n 1 10 1 2 n 1 is an infinite series. What is special about a geometric series.

So indeed the above is the formal definition of the sum of an infinite series. The sum s of an infinite geometric series with 1 r 1 is given by the formula s a 1 1 r an infinite series that has a sum is called a convergent series and the sum s n is called the partial sum of the series. Finding sums of infinite series. To find r you divide a2 by a1.

Find the sum of the infinite geometric series 36 12 4 3636 1212 44 this is a geometric sequencesince there is a common ratiobetween each term. In general in order to specify an infinite series you need to specify an infinite number of terms. Find the sum of the infinite geometric series. The infinity symbol that placed above the sigma notation indicates that the series is infinite.