Is the binomial theorem and pascal's formula the same?

1 answer:

3 0

They are closely related. The Binomial Theorem expands (a+b)ⁿ as the sum of a series of terms involving progressive powers of a and b with a coefficient based entirely on the exponent n. Coefficients of consecutive terms in the series are the same as the nth rows of Pascal’s Triangle. This means that the formula used for calculating the coefficients in the Binomial expansion is the same one used to calculate the numbers in the corresponding row of Pascal’s Triangle. The nomenclature ⁿcᵣ for the number of ways of combining r objects out of n objects invokes this formula.

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Sergio [31]

1) given
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3) definition of linear pair and supplementary
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8 0

3 years ago

What is the solution of the system of equations? y= -3x+8 y= -5x-2

Crazy boy [7]

Y = -3x+8
y = -5x-2
------------
y = 5(-3x+8)
y = 3(-5x-2)
---------------
y = -15x+40
y = -15x-6
--------------
y = -15x+40
- -
y = -15x-6
--------------
y = 46

y = -3x+8
46 = -3x+8
-8 -8
---------------
38 = -3x
---- ----
-3 -3
12.666...=x
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5 0

3 years ago

Read 2 more answers

Graph the image of square TUVW after the following sequence of transformations:

GuDViN [60]

Move the shape down by one quadrant and flip it so where “U” was at, “W” is in its place and Vice versa

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2 years ago

Find the value of sin(a/2) if cosa= 12/13

daser333 [38]

Answer: sin $\frac{a}{2}$ = ± $\frac{1}{\sqrt{26} }$

Step-by-step explanation:

We very well know that,

cos2A=1−2sin²A

⟹ sinA = ± $\sqrt{(1-} \frac{cos2A}{2} )$

As required, set A = $\frac{a}{2}$ & cos a= $\frac{12}{13}$ ,thus we get

sin $\frac{a}{2}$ =± $\sqrt{\frac{1-cos a}{2} }$

∴ sin $\frac{a}{2}$ =± $\sqrt{\frac{1-\frac{12}{13} }{2} }$ = ± $\frac{1}{\sqrt{26} }$

since ,360° < $\frac{a}{2}$ <450°

,180° < $\frac{a}{2}$ <225°

Now, we are to select the value with the correct sign. It's is obvious from the above constraints that the angle a/2 lies in the III-quadrant where 'sine' has negative value, thus the required value is negative.

hope it helped!

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2 years ago

The sum of x and 2 and itr is and algebraic expression

Masja [62]

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