Oh this one has been killing me all day, I absolutely hate using the Binomial Theorem.
The first six rows of pascal's triangle are shown below.
(insert Pascals Triangle here)
When ^{7})
is expanded into a polynomial in decreasing powers of x, from left to right, the fifth term is
I think I might have missed the relationship between the Binomial Theorem and Pascal's Triangle.
Would I look at the 5th row and add all the numbers and that is the co-eff of it?
It's a multiple choice from VCAA 2000 if anyone's curious.
also, have a pascal swirl.
Firstly, do you understand how pascal's triangle works? (I'll assume so for now and edit in later if you don't)
If it is to the power of 7 you use the numbers from the 8th row of pascals triangle (If you don't understand why (x + a)
0 will correspond to the first row)
Although, you don't need any of this I'll show you how it works for when you have a number rather than a, which will affect the coefficient:
1(x)
7(a)
0 + 7(x)
6(a)
1 + 21(x)
5(a)
2 + 35(x)
4(a)
3 + 35(x)
3(a)
4 + 21(x)
2(a)
5 + 7(x)
1(a)
6 + 1(x)
0(a)
7x
7 + 7x
6a + 21x
5a
2 + 35x
4a
3 + 35x
3a
4 + 21x
2a
5 + 7xa
6 + a
7Anywho, as "a" isn't a number, you can see the coeffcient of the 5th term is 35
edit: beaten, ah well
Consider the function f: (-infinity, -1] -> f(x) = (x-1)/ (x^2 + x + 2)
Find the rule for the inverse function f-1
This is tech-active, yeah?
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