Quiz about Ch 11.4 Warm-Up 253

Question 1

T/F: The series $$\sum_{n=1}^{\infty}\frac{1}{n}$$ converges because $$\lim_{n\rightarrow\infty}\ \frac{1}{n}=0$$ .

Accepted Answer

FALSE

Answer

TRUE

Question 2

T/F: The series $$\sum_{n=2}^{\infty}\frac{4n^2-n^3}{10+2n^3}$$ diverges because $$\lim_{n\rightarrow\infty}\ \frac{4n^2-n^3}{10+2n^3}=-\frac{1}{2}$$ .

Accepted Answer

TRUE

Answer

FALSE

Question 3

T/F: The series $$\sum_{n=3}^{\infty}\frac{4}{n^5}$$ converges by the p-series test.

Accepted Answer

TRUE

Answer

FALSE

Question 4

1, 1/4, 1/8, 1/16, ...

The numbers shown above are a

Accepted Answer

sequence

Answer

series

Question 5

-1 + 1/3 - 1/9 + 1/27 - 1/81 + ...

The numbers shown above are a

Accepted Answer

series

Answer

sequence

Question 6

The sum for the series below is ...

$$\sum_{k=1}^{\infty}\frac{\left(-1\right)^{1+k}}{2^k}$$

Accepted Answer

1/3

Answer

1

Answer

2/3

Answer

Series is not convergent

Question 7

Determine if the following series is convergent or divergent.

$$\sum_{n=1}^{\infty}\frac{1}{n}$$

Accepted Answer

divergent

Answer

convergent

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