Question: If $2^{n}$ occurs in the $2^{n - 1} - 1$ term in the expansion of \(C_{0},C_{1},C_{2},.......,C_...

Question

If $2^{n}$ occurs in the $2^{n - 1} - 1$ term in the expansion of $C_{0},C_{1},C_{2},.......,C_{n}$ , then $2.C_{1} + 2^{3}.C_{3} + 2^{5}.C_{5} + ....$

Answer 1

Solution

$(5\sqrt{5} + 11)^{2n + 1} - (5\sqrt{5} - 11)^{2n + 1}$

⇒ $= 2\left\{ 2n + 1C_{1}(5\sqrt{5})^{2n}.11 +^{2n + 1}C_{3}(5\sqrt{5})^{2n - 2} \right.\$ .

Question: If \(2^{n}\) occurs in the \(2^{n - 1} - 1\) term in the expansion of \(C_{0},C_{1},C_{2},.......,C_...

Solution