PLEASE HELP!!! (55 pts)

Mathematics

2 answers:

tia_tia [17]3 years ago

7 0

Answer:

D. 6.3 cm

Step-by-step explanation:

arc length = r * theta

theta must be in radians

72 * pi/180 = 2/5 * pi

arc length = 5 * 2/5 * ip

arc length = 2 * pi

= 6.283 cm

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

D. 6.3 cm

......

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Answer the question with explanation;

PSYCHO15rus [73]

Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

$\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0$

Therefore, by the series divergence test, the series $\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}$ diverges.

EDIT: To VectorFundament120, if $(x_n)_{n\in\mathbb N}$ is a sequence, both $\lim x_n$ and $\lim_{n\to\infty}x_n$ are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.