Let
where we assume |r| < 1. Multiplying on both sides by r gives
and subtracting this from 
gives
As n → ∞, the exponential term will converge to 0, and the partial sums will converge to
Now, we're given
We must have |r| < 1 since both sums converge, so
Solving for r by substitution, we have
Recalling the difference of squares identity, we have
We've already confirmed r ≠ 1, so we can simplify this to
It follows that
and so the sum we want is
which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Answer:
Step-by-step explanation:
From least to most likely
Honour
Simple
Bonus
Do u have an attachment?? :)
Answer: (b) exactly one plane contains a given line and a point not on the line.
Step-by-step explanation: The basic postulates of geometry are very-well known to all of us. For example-
(i) The intersection of two lines determines a point,
(ii) Two parallel lines give result to a plane,
(iii) A line and a point not on the line determines a plane, etc...
Thus, with the help of the third point, we can easily arrive at the conclusion that a given line and a point not lying on the line is contained in a plane. For example- see the attached figure, AB is a line and P is any point not on the line. They both contained in the plane ABC.
Hence, the correct option is (b).
I think it's A.cody ate two-thirds of the apple pie
