You've established that

so all you need to do is compute the integral. Rewrite the integrand as

and replace

, so that

. Then

By the fundamental theorem of calculus, this evaluates to

and so the series converges.
You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.
Answer:
x = 2
Hope it helped :D
Step-by-step explanation:
Answer:
x = 22/21 , y = 8/3
Step-by-step explanation:
The present value (PV) of a loan for n years at r% compounded t times a year where there is equal P periodic payments is given by:

Given that <span>Beth
is taking out a loan of PV = $50,000 to purchase a new home for n = 25 years at an interest rate of r = 14.25%. Since she is making the payment monthly, t = 12.
Her monthly payment is given by:

Therefore, her monthly payment is about $611.50
</span>
So u multiply each term in the first parentheses by each term in the second parentheses.
√5 √5 + 6√5-3√5 - 3x6
Now you multiply the numbers which will get u:
5+6√5 - 3√5 - 18
Then subtract:
-13 +3√5 that’s your answer