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3 years ago

What is the value of x?

Mathematics

1 answer:

Pani-rosa [81]3 years ago

7 0

Answer:

x=4

Step-by-step explanation:

Length of LJ is $8\sqrt{2} * sin(30)$ which is $4\sqrt{2}$

Now, in triangle LMJ the both angles are 45 degrees,

so $x^{2} +x^{2} =(4\sqrt{2}) ^{2}$

$2x^{2} = 2*4^{2}$

x=4

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Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1

defon

I'm guessing the series is supposed to be

$\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}$

By the ratio test, the series converges if the following limit is less than 1.

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The first $n$ terms in the numerator's denominator cancel with the denominator's denominator:

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$\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0$

which means the series converges everywhere (independently of $x$ ), and so the radius of convergence is infinite.

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