Use these properties to rewrite 7/4 + 1/2 + 5/3 + 1/3 + 1/4 + 1/2 in a way that makes the addition easier. Explain how your chan
ges simplify the addition
2 answers:
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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?
Answer: 63%
Step-by-step explanation:
<u>First step</u>
Find the 10th year rate of loss that will make the average of loss over the 10 years to equal 38.0%.
Assume this rate is x;
x = 37%
<u>Second step - Survival rate</u>
The survival rate is calculated by;
= 1 - rate of loss
= 1 - 37%
= 63%