a) Prove that the coefficient of \( x^n \) in the expansion \( (1+x)^{2n} \) is twice the coefficient of $x^n$ in the expansion \( (1+x)^{2n-1} \) .…
Class 12 Mathematics · 2081 · Solved Question with Answer
a) Prove that the coefficient of\( x^n \) in the expansion \( (1+x)^{2n} \) is twice the coefficient of $x^n$ in the expansion \( (1+x)^{2n-1} \).
b) Use De-moivre's theorem to find the square root of \( -(2 + 2\sqrt{3}i) \)
c) By using principles of mathematical induction, prove that n! < 2.