Perform the indicated operation. Be sure the answer is reduced. 3/n^2-9 + 7/3-n =

Mathematics

1 answer:

Aleks04 [339]2 years ago

4 0

This is a basic algebraic fraction question

Step 1: Factor n2-9

Step 2: Rewrite the second fraction

Step 3: Write all the numerators under the least common denominator

Step 4: Expand bracket

Step 5: Collect like terms

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Solve 152x = 36. Round to the nearest ten-thousandth. 1.7509 2.6466 0.6616 1.9091

Vlad [161]

The answer is 0.6616
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2 years ago

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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.