Math Problem Statement

Evaluate the indefinite integral ∫ ln(1 + x) dx as a power series. Then find the radius and interval of convergence.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Power Series Expansion
Radius of Convergence

Formulas

ln(1+x) = Σ (-1)^(n-1) * x^n / n for n=1 to ∞
Integral of a power series ∫ x^n dx = x^(n+1) / (n+1) + C

Theorems

Radius and Interval of Convergence (Using Ratio Test or Root Test)

Suitable Grade Level

Undergraduate Calculus

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