Limit of a sequence

2010005303

Level:

Find the limit of the following sequence.

{(\frac{(n^{2} + 4 n + 4)^{n}}{n^{2 n}})}_{n = 1}^{\infty}

Hint: The limit of the sequence

{({(1 + \frac{2}{n})}^{n})}_{n = 1}^{\infty}

e^{2}

, where

e

is the Euler number.

e^{4}

e + 4

4 e

\infty

2010005304

Level:

Find the limit of the following sequence.

{({(\sqrt[n]{0.5} + \frac{\sqrt[n]{0.5}}{n})}^{n})}_{n = 1}^{\infty}

Hint: The limit of the sequence

{({(1 + \frac{1}{n})}^{n})}_{n = 1}^{\infty}

is the Euler number

e

\frac{1}{2} e

e^{\frac{1}{2}}

\frac{1}{2} + e

\infty

2010005305

Level:

Find the limit.

lim_{n \to \infty} \frac{\sqrt{6 n^{3} - 3 n + 2}}{\sqrt{2 n^{3} + 3 n - 6}}

\sqrt{3}

- \frac{1}{3}

3

0

\infty

2010005306

Level:

Find the limit.

lim_{n \to \infty} (10^{- 1} + 10^{- 2} + \dots + 10^{- n})

\frac{1}{9}

\frac{1}{10}

\frac{9}{10}

0

\infty

2010005307

Level:

Find the limit.

lim_{n \to \infty} \frac{3 + \frac{3}{2} + \frac{3}{4} + \dots + \frac{3}{2^{n}}}{2 + \frac{2}{3} + \frac{2}{9} + \dots + \frac{2}{3^{n}}}

2

\frac{3}{2}

0

\infty

\frac{2}{3}

2010005308

Level:

Find the following limit.

lim_{n \to \infty} (\frac{1 + 2 + 3 + \dots + n}{4 n^{2} - 3})

\frac{1}{8}

\frac{1}{4}

0

\infty

2010005309

Level:

Find the limit

lim_{n \to \infty} (\frac{1 + 2 + 3 + \dots + n}{1 - 2 n^{2}}) .

- \frac{1}{4}

1

0

\infty

9000063610

Level:

Find the following limit.

lim_{n \to \infty} \frac{3 + 6 + 9 + \dots + 3 n}{6 + 12 + 18 + \dots + 6 n}

\frac{1}{2}

0

1

\infty

9000064001

Level:

Consider the sequence

{(\frac{(- 1)^{n}}{n} + 3)}_{n = 1}^{\infty}

and its limit

L

. How many terms of the sequence differ from

L

by more than

\frac{1}{50}

49

50

10

100

9000064002

Level:

Consider the convergent sequence

{(\frac{5 - n}{2 n - 1})}_{n = 1}^{\infty}

and its limit

L

. Find the index of the first term of the sequence which differs from

L

by less than

\frac{1}{100}

226

450

452

451

225

2010005303

2010005304

2010005305

2010005306

2010005307

2010005308

2010005309

9000063610

9000064001

9000064002

Events

Akce

Interests

Zajímavosti

About portal

O portálu