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2 years ago

Evaluate the sum or explain why it diverges: Sigma^infinity_k = 3(-3/2)^k

Mathematics

1 answer:

LenaWriter [7]2 years ago

8 0

Answer:

Step-by-step explanation:

Remember that in the geometric serie if | r | < 1 the serie converges and if | r | ≥1 the serie diverges.

I suppose that the serie starts at 0, so using the geometric serie with r = | $\frac{-3}{2}$ | > 1 the serie diverges.

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Strike441 [17]

Answer:

324

Step-by-step explanation:

Given:

$g(x)=4x^2+2x\\ \\f(x)=\int\limits^x_0 {g(t)} \, dt$

Find:

$f(6)$

First, find f(x):

$f(x)\\ \\=\int\limits^x_0 {g(t)} \, dt\\ \\=\int\limits^x_0 {(4t^2+2t)} \, dt\\ \\=\left(4\cdot \dfrac{t^3}{3}+2\cdot \dfrac{t^2}{2}\right)\big|\limits^x_0\\ \\=\left(\dfrac{4t^3}{3}+t^2\right)\big|\limits^x_0\\ \\= \left(\dfrac{4x^3}{3}+x^2\right)-\left(\dfrac{4\cdot 0^3}{3}+0^2\right)\\ \\=\dfrac{4x^3}{3}+x^2$

Now,

$f(6)\\ \\=\dfrac{4\cdot 6^3}{3}+6^2\\ \\=288+36\\ \\=324$

4 0

3 years ago

Diff Eq dy/dx= (ycos(x))/(1+y^2) initial condition is y(0)=1 work below ...?

Volgvan

Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
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Thus,
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5 0

3 years ago

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Reil [10]

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4 0

3 years ago

Read 2 more answers

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3 years ago

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zimovet [89]

Answer:

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Step-by-step explanation:

6 0

3 years ago