Binomial stuff:
a The third term of \(\displaystyle (1\, +\, x)^n\) is \(\displaystyle 36x^2.\) Find the fourth term.
b If \(\displaystyle (1\, +\, kx)^n\, =\, 1\, \, 12x\, +\, 60x^2\, \, ...,\) find the values of \(\displaystyle k\) and \(\displaystyle n\).
c Find \(\displaystyle a\) if the coefficient of \(\displaystyle x^{11}\) in the expansion of \(\displaystyle \left(x^2\, +\, \frac{1}{ax}\right)^{10}\) is 15.
I am stuck from the beginning. I tried using general term way:Tr+1,and gives me the equation of (n chooses 2)=36,and i don't know how to solve it
a The third term of \(\displaystyle (1\, +\, x)^n\) is \(\displaystyle 36x^2.\) Find the fourth term.
b If \(\displaystyle (1\, +\, kx)^n\, =\, 1\, \, 12x\, +\, 60x^2\, \, ...,\) find the values of \(\displaystyle k\) and \(\displaystyle n\).
c Find \(\displaystyle a\) if the coefficient of \(\displaystyle x^{11}\) in the expansion of \(\displaystyle \left(x^2\, +\, \frac{1}{ax}\right)^{10}\) is 15.
I am stuck from the beginning. I tried using general term way:Tr+1,and gives me the equation of (n chooses 2)=36,and i don't know how to solve it
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