Limit of a sequence

9000063608

Level:

Find the following limit.

lim_{n \to \infty} \frac{2^{n} + 3^{n}}{3^{n}}

1

2

3

\infty

1003047501

Level:

Find the following limit.

lim_{n \to \infty} (2 \sqrt{n} - 3)

\infty

2

- 1

0

- 3

1003047502

Level:

Find the following limit.

lim_{n \to \infty} \frac{4}{2 \sqrt{n} - 3}

0

2

\frac{1}{2}

4

\infty

1003047505

Level:

Find the following limit.

lim_{n \to \infty} (\frac{5}{\sqrt{n}} - \frac{2}{3^{n}} + \frac{(- 1)^{n}}{2 n^{2} - 1} - 7)

- 7

0

- 4

\infty

- \infty

1003047601

Level:

Find the limit

lim_{n \to \infty} (n - \sqrt{n - 1})

\infty

0

- \infty

1

\frac{1}{2}

1003047602

Level:

Choose the step to take first to efficiently evaluate the limit of the sequence

{(n - \sqrt{n^{2} - 1})}_{n = 1}^{\infty}

We expand with the expression

n + \sqrt{n^{2} - 1}

We expand with the expression

n - \sqrt{n^{2} - 1}

We expand with

n

We multiply by the expression

n + \sqrt{n^{2} - 1}

We multiply by the expression

n - \sqrt{n^{2} - 1}

We substitute

n = \infty

1003047603

Level:

Find the limit

lim_{n \to \infty} (\sqrt{4 n^{2} + 3 n} - 2 n)

\frac{3}{4}

\infty

0

- \infty

\sqrt{2}

1003047604

Level:

Choose the correct computation of the limit.

L = lim_{n \to \infty} (\sqrt{n^{2} + 3 n} - 2 n)

L = lim_{n \to \infty} n (\sqrt{1 + \frac{3}{n}} - 2) = - \infty

L = \infty - \infty = 0

L = lim_{n \to \infty} (n - 2 n) = - \infty

L = lim_{n \to \infty} (n^{2} + 3 n - 4 n^{2}) = - 3

L = lim_{n \to \infty} \frac{n^{2} + 3 n - 4 n^{2}}{\sqrt{n^{2} + 3 n} + 2 n} = \infty

1003047605

Level:

Find the limit

lim_{n \to \infty} (\sqrt{n} - \sqrt{n - 1})

0

\infty

- \infty

- 1

\sqrt{2}

1003047606

Level:

The sequence

{(\sqrt{n} (\sqrt{n} - \sqrt{n - 1}))}_{n = 1}^{\infty}

is:

convergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = \frac{1}{2}

convergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = 0

convergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = 2

divergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = \infty

divergent and it does not have an infinite limit

9000063608

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