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JEE Mains · Maths · STD 11 - 8. sequence and series
If \(0\,<\,x\,<\,1\), then \(\frac{3}{2} x^{2}+\frac{5}{3} x^{3}+\frac{7}{4} x^{4}+\ldots . .\), is equal to :
- A \(\mathrm{x}\left(\frac{1+\mathrm{x}}{1-\mathrm{x}}\right)-\log _{\mathrm{e}}(1-\mathrm{x})\)
- B \(\mathrm{x}\left(\frac{1-\mathrm{x}}{1+\mathrm{x}}\right)+\log _{\mathrm{e}}(1-\mathrm{x})\)
- C \(\frac{1-x}{1+x}+\log _{e}(1-x)\)
- D \(\frac{1+x}{1-x}+\log _{e}(1-x)\)
Answer & Solution
Correct Answer
(A) \(\mathrm{x}\left(\frac{1+\mathrm{x}}{1-\mathrm{x}}\right)-\log _{\mathrm{e}}(1-\mathrm{x})\)
Step-by-step Solution
Detailed explanation
Let \(t=\frac{3}{2} x^{2}+\frac{5}{3} x^{3}+\frac{7}{4} x^{4}+\ldots . \infty\) \(=\left(2-\frac{1}{2}\right) x^{2}+\left(2-\frac{1}{3}\right) x^{3}+\left(2-\frac{1}{4}\right) x^{4}+\ldots \infty\)…
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