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3 years ago

-3+9-27+81-243+729. Using the sigma notation to write the given sum

Mathematics

1 answer:

IgorC [24]3 years ago

5 0

Answer:

546

Step-by-step explanation:

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Use the Taylor series you just found for sinc(x) to find the Taylor series for f(x) = (integral from 0 to x) of sinc(t)dt based

Marina CMI [18]

In this question (brainly.com/question/12792658) I derived the Taylor series for $\mathrm{sinc}\,x$ about $x=0$ :

$\mathrm{sinc}\,x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}$

Then the Taylor series for

$f(x)=\displaystyle\int_0^x\mathrm{sinc}\,t\,\mathrm dt$

is obtained by integrating the series above:

$f(x)=\displaystyle\int\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}\,\mathrm dx=C+\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}$

We have $f(0)=0$ , so $C=0$ and so

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}$

which converges by the ratio test if the following limit is less than 1:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(-1)^{n+1}x^{2n+3}}{(2n+3)^2(2n+2)!}}{\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}}\right|=|x^2|\lim_{n\to\infty}\frac{(2n+1)^2(2n)!}{(2n+3)^2(2n+2)!}$

Like in the linked problem, the limit is 0 so the series for $f(x)$ converges everywhere.

7 0

3 years ago

A small box of cereal contains 10 cups of cereal. A medium box of the same cereal contains 30% more cereal than the small box. H

mario62 [17]

Answer:

13 cups

Step-by-step explanation:

If the small box has 10 cups, then:

(small) 10 cups = 100%

(medium) x cups = 130%

Now, cross multiply:

10 (130) = x (100)

1300 = 100x

x = 13

Another way to solve this is by turning 30% into a decimal:

30/100 = 0.3

10 (0.3) = 3

Now you have 30% of the 10 cups, but you need 30% more than the small box, so:

10 + 3 = 13 cups

6 0

3 years ago

What is the value of 34 square

Oksi-84 [34.3K]

Question

What is the value of 34²

Answer:

1156

Step-by-step explanation:

just multiply 34 * 34 = 1156

5 0

3 years ago

Find the amount of decrease if 68 is decreased by 15%

olya-2409 [2.1K]

I think 10.2 when I use calculater

3 0

3 years ago

Write a word phrase for the expression 10+(6-4)

WARRIOR [948]

Answer:

Ten added to the difference of six and four. Or, the difference of six and four added to ten.

Step-by-step explanation:

5 0

3 years ago