Calculus
# Limits of Sequences and Series

What is the value of \[\sum_{n=0}^{\infty} \left(2 ^{n+1}-1\right) \left(\frac{1}{9}\right)^{n}?\]

Determine the sum \[\sum_{n=1}^{\infty} 63 ^{n-1} \left(\frac{1}{8}\right)^{2n}.\]

What is the value of \[\sum_{n=0}^{\infty} \left(3 ^{n+1}-1\right) \left(\frac{1}{8}\right)^{n}?\]

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