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:
The value of y in the given equation is B. 30.
Step-by-step explanation:
y = 2x² - 4x x = 5
y = 2(5)² - 4(5) Plug 5 in for x
y = 2(25) - 20 Square 5 and multiply 4 by 5
y = 50 - 20 Multiply 2 by 25
y = 30
Hope this helps,
❤<em>A.W.E.</em><u><em>S.W.A.N.</em></u>❤
125.7 - ( - 1.82 )
125.7 + 1.82
127.52
Put it in a more simplified form