6.2 Substitution reshapes a known power series · Power Series, First Half · Visual Calculus

6.2Substitution

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Chapter 2 · Applications of Integration

2.1-2.2Areas & Slicing

2.3-2.4Shells & Arc Length

2.5Physical Applications

2.6Centers of Mass

2.7-2.9Log, Exp & Hyperbolic

Chapter 3 · Techniques of Integration

3.1-3.4Techniques I

3.5-3.7Techniques II

Chapter 5 · Sequences and Series

5.1-5.3Sequences & Series I

5.4-5.6Sequences & Series II

Chapter 7 · Parametric Equations and Polar Coordinates

7.1-7.2Parametric Curves

7.3-7.4Polar Curves

Chapter 6 · Power Series

6.1-6.2Power Series I

6.1Series function 6.1Radius disk 6.1Endpoint tests 6.2Series calculus 6.2Substitution 6.2Cauchy product 6.2Present value

6.3-6.4Power Series II

Home Calculus IISections 6.1-6.26.2 Substitution reshapes a known power series

6.2

Substitution reshapes a known power series

case

cubic0.56

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SymPy check = 0.8888888889

SymPy checks

Geometric function value at x=1/22

Example 6.1 radius of convergence3

Left endpoint alternating harmonic sum0.6931471806

Differentiated geometric value at x=1/41.7777777778

Substituted geometric value at x=1/20.8888888889

Cauchy product value at x=1/22.6666666667

Perpetuity present value at 5 percent20