The graph below shows point P and line A. If line B is drawn such that it passes through point P and is parallel to line A, what
is the equation of line B? Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms. The graph below shows point P and line A. If line B is drawn such that it passes through point P and is parallel to line A , what is the equation of line B ? Give your answer in the form y = mx + c , where m and care integers or fractions in their simplest forms .
1 answer:
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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?