I believe this question is referring to purchasing a discount on a loan's interest rate by putting more towards closing costs. For mortgages, sometimes they will allow you to "buy" a smaller interest rate. For example:
<span>Loan A has an interest rate of 4.5% and no closing costs. </span>
<span>Loan B has an interest rate of 4.375%, but has $1000 in closing costs. </span>
<span>Normally, Loan A would be the better choice if you plan on keeping the home short term, but Loan B would be more beneficial for keeping the loan long-term. I don't really care to spend the time that is necessary to come up with an actual scenario, but I hope that helps enough for you to understand the question.</span>
8x+2 it’s correct because it’s correct
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
This is an arith. sequence, and the common difference is -9.
a(n+1) = a(n)-9, with a(1)=8. Thus, if we look at the first term, we see 8; subracting 9 from 8 produces the second term (-1).
I believe the equation should be set up like this: 85 + 5x + 5x + 5x - 10 + 5x + 5 = 540. Don't forget to combine like terms! Please let me know by sending me a message if you need any more help :)
