**Find the value of an infinite geometric series :**

Infinite geometric series means the series will never end. The series which is in the form of a + ar + ar² + ar³ + ....... is called geometric series.

We have a formula to find the sum of infinite geometric series

**Example 1 :**

Find the sum of the infinite geometric series.

**Solution :**

To find the sum of the infinite geometric series, we have to use the formula a/(1- r)

here First term (a) = 1

and common ratio (r) = a₂/a₁

= (3/4) / 1

r = 3/4

sum of the given infinite series = 1/[1 - (3/4)]

= 1 / (1/4)

= 4

Hence the sum of infinite series is 4.

**Example 2 :**

Find the sum of the infinite geometric series.

**Solution :**

To find the sum of the infinite geometric series, we have to use the formula a/(1- r)

here First term (a) = 1

and common ratio (r) = a₂/a₁

= (2/3) / 1

r = 2/3

sum of the given infinite series = 1/[1 - (2/3)]

= 1 / (1/3)

= 3

Hence the sum of infinite series is 3.

**Example 3 :**

Find the sum of the infinite geometric series.

**Solution :**

To find the sum of the infinite geometric series, we have to use the formula a/(1- r)

here, first term (a) = 1

and common ratio (r) = a₂/a₁

= (1/2) / 1

r = 1/2

sum of the given infinite series = 1/[1 - (1/2)]

= 1 / (2/1)

= 2

Hence the sum of infinite series is 2.

**Example 4 :**

Find the sum of the infinite geometric series.

**Solution :**

To find the sum of the infinite geometric series, we have to use the formula a/(1- r)

here, first term (a) = 1

and common ratio (r) = a₂/a₁

= (3/5) / 1

r = 3/5

sum of the given infinite series = 1/[1 - (3/5)]

= 1 / (2/5)

= 5/2

Hence the sum of infinite series is 2.

**Example 5 :**

Find the sum of the infinite geometric series.

**Solution :**

To find the sum of the infinite geometric series, we have to use the formula a/(1- r)

here, first term (a) = 1

and common ratio (r) = a₂/a₁

= (1/4) / 1

r = 1/4

sum of the given infinite series = 1/[1 - (1/4)]

= 1 / (3/4)

= 4/3

Hence the sum of infinite series is 4/3.

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