The sequence in question is a_n = (1 + 4n)/n.

To check for convergence, we need to find the limit as n approaches infinity.

Step 1: Simplify the sequence
a_n = 1/n + 4

Step 2: Find the limit as n approaches infinity
lim (n-∞) (1/n + 4) = lim (n-∞) (1/n) + lim (n-∞) (4)

Step 3: Solve the limits
The limit of 1/n as n approaches infinity is 0, and the limit of any constant as n approaches infinity is simply the constant itself.

So, lim (n-∞) (1/n + 4) = 0 + 4 = 4

Therefore, the sequence converges to 4.

Question

The sequence in question is a_n = (1 + 4n)/n.

To check for convergence, we need to find the limit as n approaches infinity.

Step 1: Simplify the sequence
a_n = 1/n + 4

Step 2: Find the limit as n approaches infinity
lim (n->∞) (1/n + 4) = lim (n->∞) (1/n) + lim (n->∞) (4)

Step 3: Solve the limits
The limit of 1/n as n approaches infinity is 0, and the limit of any constant as n approaches infinity is simply the constant itself.

So, lim (n->∞) (1/n + 4) = 0 + 4 = 4

Therefore, the sequence converges to 4.

Knowee AI · Accepted Answer

The sequence in question is a_n = (1 + 4n)/n.

To check for convergence, we need to find the limit as n approaches infinity.

Step 1: Simplify the sequence
a_n = 1/n + 4

Step 2: Find the limit as n approaches infinity
lim (n->∞) (1/n + 4) = lim (n->∞) (1/n) + lim (n->∞) (4)

Step 3: Solve the limits
The limit of 1/n as n approaches infinity is 0, and the limit of any constant as n approaches infinity is simply the constant itself.

So, lim (n->∞) (1/n + 4) = 0 + 4 = 4

Therefore, the sequence converges to 4.

Check the convergence of < an >=< 1 + 4nn >. Find the limit of < an >.

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