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AP EAMCET · Maths · Binomial Theorem

If \(\mathrm{y}=\frac{3}{4}+\frac{3.5}{4.8}+\frac{3.5 .7}{4.8 .12}+\ldots \infty\), then

  1. A \(y^2-2 y+5=0\)
  2. B \(y^2+2 y-7=0\)
  3. C \(y^2-3 y+4=0\)
  4. D \(y^2+4 y-6=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(y^2+2 y-7=0\)

Step-by-step Solution

Detailed explanation

Let \(S = 1 + y = 1 + \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \ldots \infty\) Compare with \((1-x)^{-n} = 1 + nx + \frac{n(n+1)}{2!}x^2 + \ldots\) \(nx = \frac{3}{4}\) \(\frac{n(n+1)}{2}x^2 = \frac{15}{32}\) \(\frac{(n+1)x}{2} = \frac{15/32}{3/4} = \frac{5}{8}\)…