Using mathematical induction, prove that $${}^m{C_0}{}^n{C_k} + {}^m{C_1}{}^n{C_{k - 1}}\,\,\, + .....{}^m{C_k}{}^n{C_0} = {}^{\left( {m + n} \right)}{C_k},$$
where $$m,\,n,\,k$$ are positive integers, and $${}^p{C_q} = 0$$ for $$p < q.$$
Answer
Solve it.
4
IIT-JEE 1988
Subjective
Let $$R$$ $$ = {\left( {5\sqrt 5 + 11} \right)^{2n + 1}}$$ and $$f = R - \left[ R \right],$$ where [ ] denotes the greatest integer function. Prove that $$Rf = {4^{2n + 4}}$$
Answer
Solve it.
Questions Asked from Mathematical Induction and Binomial Theorem
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