🛠️ JEE➗ Maths

If \(0<x<1\) and \(y=\frac{1}{2} x^2+\frac{2}{3} x^3+\frac{3}{4} x^4+\ldots\), then the value of \(e^{1+y}\) at \(…

If \(0<x<1\) and \(y=\frac{1}{2} x^2+\frac{2}{3} x^3+\frac{3}{4} x^4+\ldots\), then the value of \(e^{1+y}\) at \(x=\frac{1}{2}\) is:

[JEE Main 2021, 27 Aug (Shift 2)]

\(2{e}^{2}\)

\(\frac{1}{2}{e}^{2}\)

\(2e\)

\(\frac{1}{2}\sqrt{e}\)

🔒

Answer & explanation — PYQ Pass

Options are free to see. Unlock the correct answer and full explanation with Pass.

Unlock · ₹149

See every question on Sequence and Series, or browse the full JEE question bank.

If \(0&lt;x&lt;1\) and \(y=\frac{1}{2} x^2+\frac{2}{3} x^3+\frac{3}{4} x^4+\ldots\), then the value of \(e^{1+y}\) at \(…