Let 5_ n =1+q+q^ 2 + +q^ n and T_ n =1+ ( q+1 2 )+ ( q+1 2 )^ 2 + + ( q+1 2 )^ n where q…
Mathematics · JEE Main · NTA Exams — Binomial Theorem And Its Simple Applications
Let \(5_{n}=1+q+q^{2}+\ldots+q^{n}\) and \(T_{n}=1+\left(\frac{q+1}{2}\right)+\left(\frac{q+1}{2}\right)^{2}+\ldots+\left(\frac{q+1}{2}\right)^{n}\) where q is a real number and q ≠ 1. If 101C1 + 101C2. S1 + ... + 101C101. S100 = αT100 then α is equal to
- 202
- 200
- 2100
- 299
Answer
(D) 2 99
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