Using the first several non-zero terms of the series expansion

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Using the first several non-zero terms of the series expansion ln⁡(1+x)=∑n=1∞(−1)n+1xnn\ln(1+x)=\displaystyle \sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{n}}{n}, what is the least number of non-zero terms required so that the absolute error in approximating ln⁡(1.3)\ln(1.3) is less than 0.00050.0005? (a) 66 (b) 44 (c) 33 (d) 55

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