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4 years ago

Find the sum of the geometric series 6Σ3i i=2

Mathematics

1 answer:

topjm [15]4 years ago

6 0

$\sum_{3}^{6}2=\sum_{0}^{3}2=2+2+2=\boxed{6}$

Or did you mean:

$6\times\sum{3i}=6\times\sum{6}=6\times6=\boxed{36}$

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If any one could please help

yKpoI14uk [10]

Answer:

I believe it’s the 3rd option but I’m not completely confident

Step-by-step explanation:

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3 years ago

Read 2 more answers

Greg runs 3 miles in 28 minutes. At the same rate, how many miles would he run in 42 minutes?

Paladinen [302]

Answer:

4.5

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Step-by-step explanation:

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7 0

3 years ago

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The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$