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3 years ago

Find the 20th term of the geometric sequence when A1=2 and r=2

Mathematics

1 answer:

labwork [276]3 years ago

8 0

A_n= a₁ rⁿ⁻¹

a₁ is the first term

r= common ratio

a_n=2(2)²⁰⁻¹= 1048576

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Step-by-step explanation:

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Question 5: prove that it’s =0

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Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that $\cos(\frac{2}{x})$ is a variable number between -1 and 1 (inclusive).

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By squeeze theorem, if $-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

and $\lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L$ , then we can also conclude that $\im_{x \rightarrow} x^4\cos(\frac{2}{x})=L$ .

So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at $x=0$ .

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$\lim_{x \rightarrow 0}-x^4=-0^4=-0=0$ .

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Some people call this sandwich theorem.

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