Sum of infinite series 1-1/3+1/9-1/27+.....
Answers
Answer:
The sum of the given infinite series is found to be 0.75 or .
Step-by-step explanation:
The given infinite series is as follows:
On carefully observing, we can say that the given infinite series is a geometric series with a common ratio.
Finding the common ratio, we get:
similarly,
Thus, the common ratio of the given series is .
Now, we know that the expression of the sum of infinite series is given by:
Substituting the known information, we get:
or we can say:
which gives us:
or 0.75
Thus, the sum of the given infinite series is found to be 0.75 or .
In Maths, Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
Given:
Sum of infinite terms of