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AP EAMCET · Maths · Binomial Theorem

\(1+\frac{4}{15}+\frac{4.10}{15.30}+\frac{4.10 .16}{15.30 .45}+\ldots \quad \infty=\)

  1. A \(\left(\frac{3}{5}\right)^{2 / 3}\)
  2. B \(\left(\frac{5}{3}\right)^{2 / 3}\)
  3. C \(\left(\frac{3}{5}\right)^{3 / 2}\)
  4. D \(\left(\frac{5}{3}\right)^{3 / 2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left(\frac{5}{3}\right)^{2 / 3}\)

Step-by-step Solution

Detailed explanation

\(ny = \frac{4}{15}\), \(\frac{n(n-1)}{2!}y^2 = \frac{4 \cdot 10}{15 \cdot 30} = \frac{4}{45}\) \(\frac{n-1}{2n} = \frac{4/45}{(4/15)^2} = \frac{5}{4} \implies 4(n-1)=10n \implies 6n=-4 \implies n=-\frac{2}{3}\) \((-\frac{2}{3})y = \frac{4}{15} \implies y = -\frac{2}{5}\)…