30 Questions
What is the coefficient of x^n in the expansion of e^ax?
a^n / n!
What is the value of the series 1 + x + x^2/2! + x^3/3! +...?
e^x
What is the sum of the series 1 - 1 + 1/2! - 1/3! + 1/4! -...?
1/e
What is the coefficient of x^n in the expansion of e^(-x)?
(-1)^n / n!
What is the value of the series 1 + 2x + 3x^2/2! + 4x^3/3! +...?
e^(3x)
What is the general term in the expansion of e^x?
x^n / n!
What is the coefficient of x^n in the expansion of e^x?
1 / n!
What is the value of ∑ (n=0 to ∞) n^2 / n!?
3e
What is the value of ∑ (n=1 to ∞) (2n-2)! / (2n-1)!
e/2
What is the general term in the expansion of e^(ax)?
a^n x^n / n!
What is the value of $e^x$ according to the exponential series?
1 + x + $\frac{x^2}{2!}$ + $\frac{x^3}{3!}$ +...
What is the value of $e^{-x}$ according to the exponential series?
1 - x + $\frac{x^2}{2!}$ - $\frac{x^3}{3!}$ +...
What is the value of $\frac{e^x + e^{-x}}{2}$?
1 + $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ +...
What is the value of $e - 1$?
1! + 2! + 3! + 4! +...
What is the value of $\sum_{n=0}^{\infty} $\frac{1}{n!}$?
1 + $\frac{1}{2!}$ + $\frac{1}{3!}$ + $\frac{1}{4!}$ +...
What is the general term in the expansion of log e(1+x)?
(-1)^n x^(n+1) / (n+1)
What is the coefficient of x^n in the expansion of e^(-x)?
(-1)^n / n!
What is the value of the series 1 + x - x^2/2! + x^3/3! - x^4/4! + ...?
e^(-x)
What is the sum of the series x - x^2/2! + x^3/3! - x^4/4! + ...?
log e(1+x)
What is the general term in the expansion of e^(ax)?
(ax)^n / n!
What is the value of the series ∑ (n=0 to ∞) (2n+1)! / (2n+2)?
e/2
What is the coefficient of x^n in the expansion of e^(ax)?
(ax)^n / n!
What is the value of ∑ (n=1 to ∞) (n-1)! / n!?
e - 1
What is the general term in the expansion of e^(-ax)?
(-1)^n (ax)^n / n!
What is the value of the series ∑ (n=0 to ∞) (-1)^n / n!?
1/e
What is the sum of the series 1 + x + x^2/2! + x^3/3! +...
e^x
What is the coefficient of x^(2n) in the expansion of e^x?
1/(2n!)
What is the sum of the series 1 - 1/1! + 1/2! - 1/3! + 1/4! - ...?
e^(-1)
What is the general term in the expansion of e^(ax)?
a^n x^n / n!
What is the expansion of e^(-x) according to the exponential series?
1 - x + x^2/2! - x^3/3! + ...
Test your understanding of mathematical series expansions, including the exponential function and its applications. Practice problems and examples are provided to help you master the concepts.
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