Question

For an infinite geometric progression, find the sum of number of the series known that first number of the series is one less than common ratio of G.P.
1. -1
2. \(1\over 2\)
3. 2
4. Cannot be determined

Answer 1

Correct Answer - Option 1 : -1

Concept:

Sum of the infinite G.P. = \(\rm a\over (1-r)\)

Where a is the first number and r is the common ratio

Calculation:

Let the common ratio be 'r' and the first number be 'a'

According to the question

a = r - 1

Now, the sum of the G.P. is

S = \(\rm a\over (1-r)\)

S = \(\rm r-1\over (1-r)\)

S = -1