Exponential Series

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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)?

(-1)^n / n! Signup and view all the answers

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

e^(3x) Signup and view all the answers

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

x^n / n! Signup and view all the answers

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

1 / n! Signup and view all the answers

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

3e Signup and view all the answers

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

e/2 Signup and view all the answers

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

a^n x^n / n! Signup and view all the answers

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

1 + x + $\frac{x^2}{2!}$ + $\frac{x^3}{3!}$ +... Signup and view all the answers

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

1 - x + $\frac{x^2}{2!}$ - $\frac{x^3}{3!}$ +... Signup and view all the answers

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

1 + $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ +... Signup and view all the answers

What is the value of $e - 1$?

1! + 2! + 3! + 4! +... Signup and view all the answers

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

1 + $\frac{1}{2!}$ + $\frac{1}{3!}$ + $\frac{1}{4!}$ +... Signup and view all the answers

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

(-1)^n x^(n+1) / (n+1) Signup and view all the answers

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

(-1)^n / n! Signup and view all the answers

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

e^(-x) Signup and view all the answers

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

log e(1+x) Signup and view all the answers

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

(ax)^n / n! Signup and view all the answers

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

e/2 Signup and view all the answers

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

(ax)^n / n! Signup and view all the answers

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

e - 1 Signup and view all the answers

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

(-1)^n (ax)^n / n! Signup and view all the answers

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

1/e Signup and view all the answers

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

e^x Signup and view all the answers

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

1/(2n!) Signup and view all the answers

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

e^(-1) Signup and view all the answers

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

a^n x^n / n! Signup and view all the answers

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

1 - x + x^2/2! - x^3/3! + ... Signup and view all the answers

Exponential Series

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Questions and Answers

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

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

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

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

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

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

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

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

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

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

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

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

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

What is the value of $e - 1$?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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