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Wittaler [7]
3 years ago
11

Middle term in expansion of. (x+1/x)^18​

Mathematics
1 answer:
ladessa [460]3 years ago
3 0

Answer:

Step-by-step explanation:

I used Pascal's Triangle to the 19th row (that took forever!!) and the leading coefficients are as follows:

1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1

You need the middle term so we can stop the expansion at 48,620.  We will choose an a and a b from the binomial to be a = x and b = 1/x.  Start with the coefficients from above in order and follow the pattern:

1(x)¹⁸(1/x)⁰ + 18(x)¹⁷(1/x)¹ + 153(x)¹⁶(1/x)² + 816(x)¹⁵(1/x)³ + 3060(x)¹⁴(1/x)⁴ + 8568(x)¹³(1/x)⁵ + 18564(x)¹²(1/x)⁶ + 31824(x)¹¹(1/x)⁷ + 43758(x)¹⁰(1/x)⁸ + 48620(x)⁹(1/x)⁹

That last term there is the middle term.  Simplified it looks like this:

\frac{48620x^9}{x^9} which is simplified to just 48620

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Anybody...Help!!!!!!!!!!!
Sloan [31]
Simple...

when they ask for the rate of change they ask for slope -->>

Using \frac{ y_{1} - y_{2} }{ x_{1} - x_{2} } to find the rate of change for (-3,0) and (-2,-5)

\frac{0--5}{-3--2}

\frac{0+5}{-3+2}

\frac{5}{-1}

m=-5 

Thus, your answer.


4 0
2 years ago
I am M I am a number between 17 and 25 I am a multiple of 36 is not a factor of mine what am I
Leni [432]

Answer:

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Step-by-step explanation:

8 0
2 years ago
(3-4i)(6i+7)-(2-3i)
Sergeu [11.5K]

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)}  \\  \displaystyle \large{[18i + 21  - 24 {i}^{2}  - 28i]- (2 - 3i)}

Now combine like terms.

\displaystyle \large{[ - 10i+ 21  - 24 {i}^{2} ]- (2 - 3i)}

<u>I</u><u>m</u><u>a</u><u>g</u><u>i</u><u>n</u><u>a</u><u>r</u><u>y</u><u> </u><u>U</u><u>n</u><u>i</u><u>t</u>

\displaystyle \large{i =   \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2}  =   - 1 }

Therefore:-

\displaystyle \large{[ - 10i+ 21  - 24  ( - 1) ]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 21   + 24]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

\displaystyle \large{- 10i+ 45 -  (2 - 3i)}  \\   \displaystyle \large{- 10i+ 45 -  2 + 3i}

Combine like terms.

\displaystyle \large{43 - 7i}

5 0
2 years ago
Evaluate:<br> -77 + (-46)
Firdavs [7]

Answer:

-77 + (-46)

=> -77 - 46 (When you add two negative integers, it is the same thing as subtracting a positive integer with a negative integer)

=> -123 (Because a negative + a negative = a negative)

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

6 0
3 years ago
Read 2 more answers
Does anyone know the answer to this
dolphi86 [110]

Answer:

A

Step-by-step explanation:

Hope this helps! Good Luck!

6 0
3 years ago
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