Power series Quiz 1

Question 1

If ratio test $$<1$$, then the series is:

Accepted Answer

convergent

Answer

divergent

Answer

congruent

Answer

oscillatory

Question 2

How can $$2,16,40,74...$$ be written in compact form?

Accepted Answer

$$\sum\limits_{n=0}^{\infty }{(5{{x}^{2}}+9x+2)}$$

Answer

$$\sum\limits_{n=0}^{\infty }{(5{{x}^{2}}+3x+2)}$$

Answer

$$\sum\limits_{n=0}^{\infty }{(5{{x}^{2}}+7x+4)}$$

Answer

none of the above

Question 3

What is the ratio of centres of series $$\sum\limits_{n=0}^{\infty }{\dfrac{{{(-2)}^{n}}}{(n+1)!}{{\left( \dfrac{x+3}{2} \right)}^{n}}}$$ and $$\sum\limits_{n=0}^{\infty }{\dfrac{{{(-4)}^{n}}}{(n+2)!}{{\left( x+3 \right)}^{n}}}$$?

Accepted Answer

$$1:1$$

Answer

$$2:1$$

Answer

$$4:1$$

Answer

$$1:4$$

Question 4

What is the radius and interval of convergence of $$\sum\limits_{n=0}^{\infty }{{{(2x-9)}^{n}}}$$?

Accepted Answer

$$\dfrac{1}{2},(4,5)$$

Answer

$$\dfrac{1}{2},(5,6)$$

Answer

$$\dfrac{1}{3},(4,5)$$

Answer

$$\dfrac{1}{3},(5,6)$$

Question 5

What is the Taylor series for $$f(x)=\dfrac{1}{a+x}$$ with centre at $$x=0$$?

Accepted Answer

None of the above

Answer

$$\dfrac{1}{a}-\dfrac{1}{{{a}^{2}}}x+\dfrac{1}{{{a}^{3}}}{{x}^{2}}-\dfrac{1}{{{a}^{4}}}{{x}^{3}}...$$

Answer

$$\dfrac{1}{a}+\dfrac{1}{{{a}^{3}}}{{x}^{2}}...$$

Answer

$$\dfrac{1}{a}x-\dfrac{1}{{{a}^{2}}}{{x}^{2}}+\dfrac{1}{{{a}^{3}}}{{x}^{3}}-\dfrac{1}{{{a}^{4}}}{{x}^{4}}...$$