# Science:Infinite Series Module/Quizzes/Quiz Questions

## Quiz 1

### Question 1

${\displaystyle a_{k}=\sin {\Bigg (}{\frac {2\pi k}{4+4k}}{\Bigg )}}$

${\displaystyle {\frac {1}{\sqrt {2}}}}$

### Question 2

${\displaystyle \sum _{k=2}^{\infty }{\frac {4^{k-2}}{5^{k-1}}}}$

### Question 3

${\displaystyle \sum _{k=1}^{\infty }{\Bigg (}{\frac {1}{k+4}}-{\frac {1}{k+5}}{\Bigg )}}$

### Question 5

${\displaystyle a_{n}={\begin{cases}2-{\frac {1}{n}}&{\text{if }}n{\text{ is odd}}\\1+{\frac {1}{n}}&{\text{if }}n{\text{ is even}}\end{cases}}}$

## Quiz 2

### Question 1

${\displaystyle {\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{7}}+\ldots }$

### Question 2

${\displaystyle \sum _{k=1}^{\infty }{\frac {(x-1)^{k}(k+2)}{2^{k}(k+3)}}}$

### Question 3

${\displaystyle \sum _{k=1}^{\infty }\ln {\Bigg (}{\frac {k^{2}+3}{k^{2}+2k+4}}{\Bigg )}}$

### Question 4

${\displaystyle \sum _{k=1}^{\infty }{\frac {k^{k}}{(3k)!}}}$

### Question 5

${\displaystyle \sum _{k=1}^{\infty }{\frac {(-1)^{k}}{k-p}}}$

## Quiz 3

### Question 1

${\displaystyle f(x)={\frac {4}{16x^{2}-1}}}$

### Question 2

${\displaystyle f(x)=e^{5x}\cos(5x)}$

### Question 3

Equation 1

${\displaystyle \int e^{-x^{2}}dx}$

Equation 2

${\displaystyle D+x+{\frac {x^{3}}{a}}+\ldots }$

### Question 4

${\displaystyle f(x)={\frac {\sin(2x)}{3x}}}$

### Question 5

${\displaystyle \sum _{k=0}^{\infty }{\frac {x^{8k}}{k!}}}$