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Tests of Convergence and Divergence
If one test is inconclusive, try a different test. There is no single test that must be used on a given series.
Taylor Polynomial
What is the general form of a Taylor polynomial for f(x) centered at x=c?
Taylor Series vs. Taylor Polynomial
What is the difference between a Taylor series and a Taylor polynomial?
Taylor Polynomial: Finite sum up to the n-th term.
Taylor Series: Infinite sum (if it converges to f(x)).
Taylor Remainder (Error Term)
How is the error Rn(x) of a Taylor polynomial defined?
Lagrange Error: Use when you need a worst-case error estimate for Taylor approximations.
Alternating Series: For series like ∑(−1)nan, the error is always less than the next term.
Maclaurin Series