Binomial Series - Ambitious

Question 1: Find the value of

\frac{16!}{13!}

A

\frac{16}{13}

B

240

C

3360

D

0

Question 2: Find the value of

\frac{4!}{0!}

A

Does not exist

B

0

C

1

D

24

Question 3: Knowing that combinational coefficient

C_{r}^{n} = \frac{n!}{(n - r)! r!}

, find

C_{1}^{5}

A

1

B

0

C

5

D

25

Question 4: Simplify:

\frac{(3 n)!}{(3 n + 2)!}

A

\frac{1}{(3 n + 3) (3 n + 2)}

B

\frac{1}{{(3 n + 3)}^{2}}

C

\frac{1}{(3 n + 2) (3 n + 1)}

D

\frac{3 n}{3 n + 2}

Question 5: Find the coefficient of

x^{4}

in the binomial expansion of

{(2 - \frac{3}{x})}^{9}

A

\frac{326592}{x^{4}}

B

\frac{647378}{x^{4}}

C

\frac{353682}{x^{4}}

D

\frac{1}{x^{4}}

Question 6: Find the

7

th term of

{(3 - \frac{x}{4})}^{13}

in the binomial expansion

A

\frac{1}{3} x^{6}

B

\frac{2}{5} x^{6}

C

\frac{938223 x^{6}}{1024}

D

\frac{3}{7} x^{6}

Question 7: Write down the sum of the first n terms using sigma notation of the following series:

- 1 + 2 - 3 + 4 - 5 + 6 - 7 + 8...

A

\sum_{n = 1}^{n} (- 1) n^{n}

B

\sum_{n = 1}^{n} (- 1) n

C

\sum_{n = 1}^{n} - n

D

\sum_{n = 1}^{n} {(- 1)}^{n} n

Question 8: Find the value of

\sum_{n = 1}^{70} n

A

140

B

2500

C

70

D

2485

Question 9: Find the value of

\sum_{r = 1}^{n} (18 r + 3)

A

9 n^{2} + 3

B

3 n (3 n^{2} + 4)

C

18 n^{2} + 4

D

n (3 n^{2} + 3)

Question 10: Knowing binomial expansion of

e^{x}

find

e^{0.41}

by calculating first

5

terms in the series

A

1.5067144

B

1.603416

C

1.497722

D

1.57568

Test: Binomial Series - Ambitious

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