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Artist 52 [7]
3 years ago
12

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

Mathematics
1 answer:
defon3 years ago
3 0
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.

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|

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

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

|x^n| also cancels out and the remaining factor of |x| can be pulled out of the limit (as it doesn't depend on n).

\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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Answer:

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Step-by-step explanation:

the difference is  about 16.25$

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The water in a reservoir decreased by 47% during a drought. Before the drought, the reservoir held 44,580 acre ft (AF) of water.
RSB [31]


44,580 x 47 %

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If you want the water level after the drought just subtract.

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Hope this helps. :)

5 0
3 years ago
A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school coll
Mademuasel [1]

Amount of money collected in the 2-day fundraiser is represented by the following equations:

  • 12x + 4y = 152 .................. (i)
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where x is the cost of a chicken lunch and y is the cost of a vegetarian lunch

Multiplying (i) with 3 and subtracting it from (ii)

36x + 12y - (32x + 12y) = 456 - 420

⇒ 4x = 36

⇒ x = 9

Put value of x in (i)

⇒ 12 × 9 + 4y = 152

⇒ 108 + 4y = 152

⇒ 4y = 44

⇒ y = 11

Hence, cost of the vegetarian meal is 11.

7 0
3 years ago
Richard bought 32.4 pounds of potting soil and 45.6 pounds of sand. She got the potting soil for $0.86 per pound and the sand fo
frozen [14]

Answer:

67.00

Step-by-step explanation:

Add the numbers.

You get 67.08.

You want it rounded.

So now the answer is 67.00.

3 0
3 years ago
how much would $500 invested at 6% interest compounded continuously be worth after 4 years? round your answer to the nearest cen
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A=pe^rt
A=500×e^(0.06×4)
A=635.62
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3 years ago
Read 2 more answers
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