Exponential Series
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Questions and Answers

What is the coefficient of x^n in the expansion of e^ax?

  • a^n / n! (correct)
  • n!/n!
  • n!
  • 1/n!

What is the value of the series 1 + x + x^2/2! + x^3/3! +...?

  • e^x (correct)
  • e^(-x)
  • 1/e^x
  • 1 - e^x

What is the sum of the series 1 - 1 + 1/2! - 1/3! + 1/4! -...?

  • e - 1
  • 1/e (correct)
  • 1 - e
  • e

What is the coefficient of x^n in the expansion of e^(-x)?

<p>(-1)^n / n! (D)</p> Signup and view all the answers

What is the value of the series 1 + 2x + 3x^2/2! + 4x^3/3! +...?

<p>e^(3x) (C)</p> Signup and view all the answers

What is the general term in the expansion of e^x?

<p>x^n / n! (C)</p> Signup and view all the answers

What is the coefficient of x^n in the expansion of e^x?

<p>1 / n! (B)</p> Signup and view all the answers

What is the value of ∑ (n=0 to ∞) n^2 / n!?

<p>3e (B)</p> Signup and view all the answers

What is the value of ∑ (n=1 to ∞) (2n-2)! / (2n-1)!

<p>e/2 (A)</p> Signup and view all the answers

What is the general term in the expansion of e^(ax)?

<p>a^n x^n / n! (B)</p> Signup and view all the answers

What is the value of $e^x$ according to the exponential series?

<p>1 + x + $\frac{x^2}{2!}$ + $\frac{x^3}{3!}$ +... (B)</p> Signup and view all the answers

What is the value of $e^{-x}$ according to the exponential series?

<p>1 - x + $\frac{x^2}{2!}$ - $\frac{x^3}{3!}$ +... (A)</p> Signup and view all the answers

What is the value of $\frac{e^x + e^{-x}}{2}$?

<p>1 + $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ +... (A)</p> Signup and view all the answers

What is the value of $e - 1$?

<p>1! + 2! + 3! + 4! +... (A), 1! + 2! + 3! + 4! +... (B)</p> Signup and view all the answers

What is the value of $\sum_{n=0}^{\infty} $\frac{1}{n!}$?

<p>1 + $\frac{1}{2!}$ + $\frac{1}{3!}$ + $\frac{1}{4!}$ +... (A)</p> Signup and view all the answers

What is the general term in the expansion of log e(1+x)?

<p>(-1)^n x^(n+1) / (n+1) (C)</p> Signup and view all the answers

What is the coefficient of x^n in the expansion of e^(-x)?

<p>(-1)^n / n! (D)</p> Signup and view all the answers

What is the value of the series 1 + x - x^2/2! + x^3/3! - x^4/4! + ...?

<p>e^(-x) (D)</p> Signup and view all the answers

What is the sum of the series x - x^2/2! + x^3/3! - x^4/4! + ...?

<p>log e(1+x) (C)</p> Signup and view all the answers

What is the general term in the expansion of e^(ax)?

<p>(ax)^n / n! (B)</p> Signup and view all the answers

What is the value of the series ∑ (n=0 to ∞) (2n+1)! / (2n+2)?

<p>e/2 (D)</p> Signup and view all the answers

What is the coefficient of x^n in the expansion of e^(ax)?

<p>(ax)^n / n! (B)</p> Signup and view all the answers

What is the value of ∑ (n=1 to ∞) (n-1)! / n!?

<p>e - 1 (A)</p> Signup and view all the answers

What is the general term in the expansion of e^(-ax)?

<p>(-1)^n (ax)^n / n! (C)</p> Signup and view all the answers

What is the value of the series ∑ (n=0 to ∞) (-1)^n / n!?

<p>1/e (C)</p> Signup and view all the answers

What is the sum of the series 1 + x + x^2/2! + x^3/3! +...

<p>e^x (A)</p> Signup and view all the answers

What is the coefficient of x^(2n) in the expansion of e^x?

<p>1/(2n!) (D)</p> Signup and view all the answers

What is the sum of the series 1 - 1/1! + 1/2! - 1/3! + 1/4! - ...?

<p>e^(-1) (B)</p> Signup and view all the answers

What is the general term in the expansion of e^(ax)?

<p>a^n x^n / n! (D)</p> Signup and view all the answers

What is the expansion of e^(-x) according to the exponential series?

<p>1 - x + x^2/2! - x^3/3! + ... (C)</p> Signup and view all the answers

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