Determine whether the sequence converges or diverges. If it converges, find the limit (if an answer does not exist, enter DNE.) {lnn/ln3}
limn→[infinity]{lnn/ln3n}=

The sequence converges. The limit DNE.

Step-by-step explanation:

Find the limit of n as n tends to infinity (in other words, positive infinity) in {Ln(n)/ Ln(3n)}

Positive infinity values for n start from 1,2,3,4,5,6,7,8,9,10,11,12,13,14,...,infinity

So I solved for values of n, up to n=20. All values are rounded up to 3 decimal places; for better accuracy.

When n is 1, the function is equal to 0.000

When n is 2, the function is = 0.387

When n is 3, the function = 0.500

When n is 4, the function = 0.558

When n is 5, the function = 0.594

When n is 6, the function = 0.619

When n is 7, the function = 0.639

When n is 8, the function = 0.654

When n is 9, the function = 0.667

When n is 10, the function = 0.677

When n is 11, the function = 0.686

When n is 12, the function = 0.693

When n is 13, the function = 0.700

When n is 14, the function = 0.706

When n is 15, the function = 0.711

When n is 16, the function = 0.716

When n is 17, the function = 0.721

When n is 18, the function = 0.725

When n is 19, the function = 0.728

When n is 20, the function = 0.732

We say there is a convergence because the space between the values of n gets smaller and smaller as n tends to infinity and there is no definite limit. Limit DNE.

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