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AP Calculus BC - Series

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Section 1

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Alternating Series Remainder

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Calculus Math

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Date created

Mar 14, 2020

Cards (24)

Section 1

(24 cards)

Alternating Series Remainder

Front

Back

e^x series

Front

1 + x/1! + x^2/2! + x^3/3! + ..... x^n/n!

Back

Absolute and Conditional Convergence

Front

Back

Nth Term Test

Front

Only determines if series diverges

Back

Taylor Series

Front

Back

Lagrange Error Bound

Front

The value between f(x) and Pn(x)

Back

Harmonic Series

Front

Back

ln(1+x) series

Front

x - x^2/2 + x^3/3 -....(-1)^n+1 (x^n)/n

Back

Maclaurin Series

Front

A Taylor Series centered around x=0

Back

Telescoping Series

Front

Use if there are two quotients

Back

sinx series

Front

x - x^3/3! + x^5/5! -.....(-1)^n x^(2n+1)/(2n+1)!

Back

Power Series Operations

Front

You can derive and integrate power series in much the same way you can derive an integrate a polynomial

Back

cosx series

Front

1 - x^2/2! + x^4/4! - ...(-1)^n (x^2n)/(2n)!

Back

1/(1+x) series

Front

1 - x + x^2 - x^3..... (-x)^n

Back

Geometric Series Test

Front

a = plugging the 'n' term into the equation

Back

1/(1-x) series

Front

1 + x + x^2 + x^3 .... x^n

Back

Ratio Test

Front

Back

Radius of Convergence

Front

Half of the distance of the convergence of a power series

Back

Limit Comparison Test

Front

Back

p-Series

Front

Back

arctanx series

Front

x - x^3/3 + x^5/5.... (-1)^n-1 (x^2n-1)/(2n-1)

Back

Alternating Series Test

Front

Back

Direct Comparison Test

Front

Back

Integral Test

Front

If integral converges: series converges If integral diverges: series diverges

Back