QUICK ILL GIVE YOU 30 PTS IF YOU CAN SOLVE IT WITH A CLEAR EXPLANATION
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The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
<h3>What is convergent of a series?</h3>A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We can find the interval for the convergent by root test.
Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.
For the given series:
As the series goes infinitely, we can use root test.
By the root test, the convergence interval will be;
The interval of convergence is:
x < -3 or x > 3 we can write this as:
|x| < 3
Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
Learn more about the convergent of a series here:
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Answer:
- a = 4/3 and b = 0
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<h2>Given expression:</h2>Bring both fractions into common denominator:
Simplify:
Compare the result with given expression to get:
- a = 4/3 and b = 0
Answer:
B) 8 and 24.
Step-by-step explanation:
Just by looking at the answer choices, since one number must be three times the other, we can determine that the correct answer is B.
Regardless, let's work this out mathematically. Let the first number be <em>a</em> and the second number be <em>b</em>.
Their difference is 16. Hence:
The first number is three times the second number. So:
Substitute:
Solve for <em>b</em>. Subtract:
And divide both sides by two:
So, the second number is 8.
And since the first number is three times the second, the first number is 24.
Our answer is B as expected.