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3 years ago

Solve the following 1/2a + b If a=10 b = 7 *

Mathematics

2 answers:

Westkost [7]3 years ago

4 0

Answer:

Step-by-step explanation:

1/2a+b=

1/2*10 + 7 =

5+7= 12

olga_2 [115]3 years ago

3 0

Answer:

1/2 × 10 + 7

=5+7

=12

..................

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(a) Suppose anxn has finite radius of convergence R and an ≥ 0 for all n. Show that if the series converges at R, then it also c

valina [46]

Answer:

a) See the proof below.

b) $\sum \frac{(-x)^n}{n}$

Step-by-step explanation:

Part a

For this case we assume that we have the following series $\sum a)n x^n$ and this series has a finite radius of convergence $R$ and we assume that $a_n \geq 0$ for all n, this information is given by the problem.

We assume that the series converges at the point $x= R$ since w eknwo that converges, and since converges we can conclude that:

$\sum a)n R^n < \infty$

For this case we need to show that converges also for $x=-R$

So we need to proof that $\sum a_n (-R)^n < \infty$

We can do some algebra and we can rewrite the following expression like this:

$\sum a_n (-R)^n = \sum (-1)^n a)n R^n$ and we see that the last series is alternating.

Since we know that $\sum a_n x^n$ converges then the sequence { $a_n R^n$ } must be positive and we need to have $lim_{n\to \infty} a^n R^n = 0$

And then by the alternating series test we can conclude that $\sum a_n (-R)^n$ also converges. And then we conclude that the power series $a_n x^n$ converges for $x=-R$ ,and that complete the proof.

Part b

For this case we need to provide a series whose interval of convergence is exactly (-1,1]

And the best function for this $\frac{(-x)^n}{n}$

Because the series $\sum \frac{(-x)^n}{n}$ converges to $-ln(1+x)$ when $|x|$ using the root test.

But by the properties of the natural log the series diverges at $x=-1$ because $\sum \frac{1}{n} =\infty$ and for $x=1$ we know that converges since $\sum \frac{-1}{n}$ is an alternating series that converges because the expression tends to 0.

6 0

3 years ago

The mean temperature for the first 7 days in January was 4 °C.

Ronch [10]

Answer:

Total temperatures for 8 days is 15.

The 8-day average (mean) temperature is 15/8 or 1.875 degrees.

Step-by-step explanation:

yeah

5 0

3 years ago

13 + 2k = 3k + 4(k - 3)

Trava [24]

Answer:

k=5

Step-by-step explanation:

−

Move all terms containing

to the left side of the equation.

8 0

4 years ago

Lester deposits $80 into a new savings account. The account earns 6.5% simple interest per year. No money is added or removed fr

Sedaia [141]

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$80\\ r=rate\to 6.5\%\to \frac{6.5}{100}\dotfill &0.065\\ t=years\dotfill &3 \end{cases} \\\\\\ A=80[1+(0.065)(3)]\implies A=80(1.195)\implies A=95.6$