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2 years ago

6

Which of the following represents the sum of the series below?

1 answer:

hoa [83]2 years ago

5 0

4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 + 31 + 34 + 37 + 40 = 286

I hope this helps!

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Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

Every month, a company increases its sales by twice the previous month. The company experienced 23 sales in January, 46 sales in

wariber [46]

23, 46, 92, 184, 368, 736, 1472, 2944, 5888.

The company will have 5888 sales.

3 0

3 years ago

What is an equation of the line that passes through the points (0, -1)(0,−1) and (6, 1)(6,1)?

horrorfan [7]

$slope = y2 - y1 \div x2 - x1$

$1 - - 1 \div 6 - 0$

$2 \div 6$

$1 \div 3$

$y = mx + c$

$1 = 1 \div 3 \times 6 + c$

$1 = 2 + c$

$c = 3$

$y = 1 \div 3x + 3$

5 0

3 years ago

Five less than three times a number

Radda [10]

That would turn into 3x-5

4 0

2 years ago

The following data shows the changes in tempreatures across varius cities from moorning to noon. which city recorded the maximum

fgiga [73]

25 because it is cool and it is the maximum weather in the earth totally

6 0

3 years ago