2 years ago

Evaluate the expression when c=4,d=6 and e=10

Mathematics

1 answer:

natima [27]2 years ago

6 0

Errrmmm.... Where is the expression?

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Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (e

Bingel [31]

Assuming the series is

$\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}$

The series will converge if

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

We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|$

So the series will certainly converge if $-1$ , but we also need to check the endpoints of the interval.

If $x=1$ , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if $x=-1$ , by the alternating series test we can show that the series converges, since

$\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0$

and is strictly decreasing.

So, the interval of convergence for the series is $-1\le x$ .

6 0

3 years ago

I had $25 and i bought 3 boxes of granola bars. i can home with $4. how much does each box of granola bars cost?

Snezhnost [94]

$25 - $4 = $21
You spent $21 on 3 boxes of granola bars.

3 boxes = $21
1 box = $21 ÷ 3 = $7

One box of granola bar costs $7.

4 0

3 years ago

Read 2 more answers

The difference of 17 and 5 tines a number

emmasim [6.3K]

You can answer this problem in two different ways: the first being (17 - 5) * x, and the second being 12 * x.

6 0