For the series

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For the series ∑n=1∞(−1)n+123n\displaystyle\sum_{n=1}^{\infty}(-1)^{n+1}\dfrac{2}{3^{n}}, let S3S_3 denote the sum of the first three terms. (a) Calculate an interval that is guaranteed to contain the exact value of the infinite series. Provide your answer in exact fractional form.

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