Sn= (N/2)(A1 + An)
I have no idea how to do these:
A) "Find the sum of the arithmetic series"
B) "Expand (x+2)^4"
So far, all I could manage to get is 1x^4(2)^0+4/1x^3(3). Is there an easier way to do this question without it becoming so messy/confusing?
Thanks in advance!
Define
[nCr] = n!/[(n - r)!r!]
Then
(x + a)^n = [nC0]*x^n*a^0 + [nC1]*x^{n - 1}*a^1 + [nC2]*x^{n - 2}*a^2 + ... + [nC(n-1)]*x^1*a^{n - 1} + [nCn]*x^0*a^n
In your case:
(x + 2)^4 = [4C0]x^4 + [4C1](2)x^3 + [4C2](2)^2x^2 + [4C3](2)^3x + [4C4](2)^4
Now
[4C0] = 1
[4C1] = 4
[4C2] = 6
[4C3] = 4
[4C4] = 1
So
(x + 2)^4 = x^4 + 4*2x^3 + 6*4x^2 + 4*8x + 16
= x^4 + 8x^3 + 24x^2 + 32x + 16
-Dan