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9000063404

Level:

Evaluate the following infinite sum.

\frac{5}{2} + \frac{5}{8} + \frac{5}{32} + \frac{5}{128} + \dots

\frac{10}{3}

5

4

\frac{5}{2}

9000063803

Level:

We are given the sequence

{(\cos n \frac{π}{4})}_{n = 1}^{\infty}

. Find the sum of the first six terms of this sequence.

- \frac{2 + \sqrt{2}}{2}

- \frac{\sqrt{2}}{2}

- 1

0

9000063804

Level:

We are given the sequence

{(\log 10^{n})}_{n = 1}^{\infty}

. Find the product of the first five terms of this sequence.

120

0

5

6

9000063807

Level:

Among the numbers

5

15

28

47

identify the number which is not a member of the sequence

{(2 n^{2} - 3)}_{n = 1}^{\infty}

28

5

15

47

9000063810

Level:

Consider the sequences

{(a_{n})}_{n = 1}^{\infty}

and

{(b_{n})}_{n = 1}^{\infty}

where

a_{n} = 2^{n}

and

b_{n} = n^{2} - 1

, respectively. Identify a true statement in the terms of these sequences.

a_{3} = b_{3}

a_{2} = b_{2} + 2

a_{4} = b_{4} - 2

a_{5} = b_{5} - 8

9000063401

Level:

Identify the quotient of the geometric series

\sum_{n = 1}^{\infty} \frac{1}{2^{n - 3}}

\frac{1}{2}

2

1

\frac{1}{8}

9000063402

Level:

Identify the quotient of the geometric series

\sum_{n = 1}^{\infty} 3^{2 - n}

\frac{1}{3}

1

\frac{1}{9}

- \frac{1}{9}

9000062401

Level:

Find the derivative of

f (x) = 3 x^{4} - 2 x^{3} - 3 x^{2}

at the point

x_{0} = - 1

- 12

0

12

24

9000062402

Level:

Find the second derivative of

f (x) = x^{4} - 3 x^{2}

at the point

x_{0} = 1

6

- 2

- 6

1

9000062404

Level:

Evaluate the following limit.

lim_{x \to + \infty} \frac{x^{3} - x + 1}{1 - x^{2} - x^{3}}

- 1

0.5

- 0.5

1

A

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