The common ratio of a ggeometric progression is r the first term of the progression is(r^2-3r+2) and the sum of infinity is S Show that S=2-r (I have) Find the set of possible values that S can take?
2 Answers
Since
Explanation:
We have
The general sum of an infinite geometric series is
In our case,
Geometric series only converge when
Explanation:
Where
We are told common ratio is
First term is
The sum of a geometric series is given as:
For the sum to infinity this simplifies to:
We are told this sum is S.
Substituting in our values for a and r:
Factor the numerator:
Multiply numerator and denominator by
Cancelling:
To find the possible values we remember that a geometric series only has a sum to infinity if
i.e.