The sequence

wurmiana6d
2021-11-16
Answered

To find: The sum of the given arithmetic sequence.

The sequence$2\sum n=1802n-5$

The sequence

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oces3y

Answered 2021-11-17
Author has **21** answers

Formula used:

The formula for the summation of a polynomial with degree 1 is,

The formula for the summation of a constantis,

Calculation:

To find the sum of the arithmetic sequence, i.e, to find,

Write

Now to find

Substitute the values of n in equation (1).

We get,

Now to find the

Substitute the values of n in equation (2).

We get,

Then,

Hence

asked 2021-03-02

Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution.
a. $\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$
b. $3,8,13,18,...,48$

asked 2020-11-10

asked 2021-12-19

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.

$P\left(x\right)={x}^{3}-4{x}^{2}-19x-14$

asked 2022-03-21

Looking for help understanding the asymptotic expansion of the digamma function

I was recently given an example using this asymptotic expansion of the digamma function where:

$\frac{d}{dx}\left(\mathrm{ln}\mathrm{\Gamma}\left(x\right)\right)=\psi \left(x\right)\sim \mathrm{ln}\left(x\right)-\frac{1}{2x}-\frac{1}{12{x}^{2}}$

Here's the example:

$\frac{\psi \left(\frac{x}{4}\right)}{4}-\frac{\psi (\frac{x}{5}+\frac{1}{2})}{5}-\frac{\psi (\frac{x}{20}+\frac{1}{2})}{20}\sim -\frac{\mathrm{ln}\left(4\right)}{4}+\frac{\mathrm{ln}\left(5\right)}{5}+\frac{\mathrm{ln}\left(20\right)}{20}-\frac{1}{2x}-\frac{11}{8{x}^{2}}$

I'm unclear on the following points:

What happened to each x term?

Why is the first term negative and the rest of the terms positive? Why isn't the signs of the original terms would be preserved?

I would have expected something like this:

$\frac{\mathrm{ln}\left(\frac{x}{4}\right)}{4}-\frac{\mathrm{ln}\left(\frac{x}{4}\right)}{4}-\frac{\mathrm{ln}\left(\frac{x}{4}\right)}{4}-\dots$

How is$\frac{11}{8{x}^{2}}$ being determined? Why does $-\frac{1}{12{x}^{2}}$ change but $-\frac{1}{2x}$ stays the same?

Sorry for the elementary questions. The explanation will really help! :-)

Thanks,

I was recently given an example using this asymptotic expansion of the digamma function where:

Here's the example:

I'm unclear on the following points:

What happened to each x term?

Why is the first term negative and the rest of the terms positive? Why isn't the signs of the original terms would be preserved?

I would have expected something like this:

How is

Sorry for the elementary questions. The explanation will really help! :-)

Thanks,

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Find a polar equation for the curve represented by the given cartesian equation.

$y=2$

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Which of the following is the correct factorization of ${x}^{3}+8$ ?