Please explain these in details and justification for each answer, thanks! 4 poi

Question

Please explain these in details and justification for each answer, thanks! 4 points) Match each sequence below to statement that BEST fits it. Z: The sequence converges to zerc L. The sequence diverges to positive infinity; F: The sequence has a finite non-zero limit D. The sequence diverges, but not to infinity. Note: On tests and quizzes, you will be expected to provide a valid mathematical justification for each answer! 1, (5n 2. 3, 100r2+1 n! 5, cos2 (n) + si (n +4n- n() 7. 10 In(n) Note: You can earn partial credit on this problem. You are in the Reduced Scoring Period: All additional work done counts 70% of the original. Preview My Answers Submit Answers Your score was recorded You have attempted this problem 2 times.

Explanation / Answer

1)
When we simplify that,
the exponents get multiplied

The exponents 2n * 1/n becomes 2n/n ---> 2

So, we get 5n^2, which DIVERGES

So, I

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2)
5^n / n!
We know that n! grows faster than 5^n

So, as n ---> inf, we get :
large value divided by much much larger value

.. which equals 0

Z

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3)
100n^2 + 1 obviously grows much faster than 3n!
So, positive infinity
I

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5)
cos^2n + sin^2n
We know full well this equals ONE
So, F

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