The sum of the series 1- 1 2 ( 1 2 )+ 1 2 3 4 ( 1 2 )^ 2 - ( 1 2 ) ( 3 4 ) ( 5 6 ) ( 1 2…
Mathematics · JEE Main · NTA Exams — Binomial Theorem And Its Simple Applications
The sum of the series \(1-\frac{1}{2}\left(\frac{1}{2}\right)+\frac{1}{2} \times \frac{3}{4}\left(\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)\left(\frac{3}{4}\right)\left(\frac{5}{6}\right)\left(\frac{1}{2}\right)^{3}+\ldots\) is :
- \(\frac{\sqrt{3}}{2}\)
- \(\sqrt{\frac{2}{3}}\)
- \(\sqrt{\frac{1}{3}}\)
- \(\frac{1}{3}\)
Answer
(B) 2 3
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