Series
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| 1-x+x^2-....+(-x)^n | 1/1+x
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| x-x^3/3!+x^5/5!-....+(-1)^n(x^2n+1)/(2n+1)! | sin(x)
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| 1+x+x^2/2!+....+x^n/n! | e^x
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| 1+x+x^2+....+x^n | 1/1-x
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| 1-x^2/2!+x^4/4!-...+(-1)^n(x^2n)/(2n)! | cos(x)
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| x-x^2/2+x^3/3-....+(-1)^n(x^n)/n | ln(1+x)
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| f(0)+f'(0)x+f"(0)x^2/2!..... | (Power)Taylor Series generated by f at x=0
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| f(a)+f'(a)(x-a)+f"(a)(x-a)^2/2! | (Power) Taylor Series generated by f at x=a
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| Sequence | a succession of numbers in order
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| Series | the sum of a sequence
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| Series in which each term is obtained by adding a constant to the precedin term. | Arithmetic series
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| Series in which each term is obtained by multiplying the preceding term by a constant | Geometric series
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| Series in which the terms alternate between positive and negative | Alternating series
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| 1/1+1/2+1/3+1/4+1/5+1/6+1/7.... | Harmonic series
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| Series that has infinitely many terms. | Infinite series
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| the sum of the first n terms of a series. | Partial sum
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| An infinite series that has a limit as n approches infinity. | Convergent series
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| An infinite series that has no limit as n approches infinity. | Divergent series
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| An infinite Geometric series converges to? | a/(1-r) when |r|=1
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| What is an Interval of Convergence? | The interval on which the series (polynomial) represents the function. (sum)
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| What is the Radius of convergence? | The radius of convergence is half the length of the interval of convergence.
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| What is the center of convergence? | The midpoint of the interval of convergence.
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| Does the harmonic series converge or diverge? | always diverges.
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| Where does an Alternating Series converge? | Converges if 1) |a1|>|a2|>|a3| or
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You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
Lone_Rider
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