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What is the value of ∑n=0∞(2n+1−1)(19)n?\sum_{n=0}^{\infty} \left(2 ^{n+1}-1\right) \left(\frac{1}{9}\right)^{n}?n=0∑∞(2n+1−1)(91)n?
Determine the sum ∑n=1∞63n−1(18)2n.\sum_{n=1}^{\infty} 63 ^{n-1} \left(\frac{1}{8}\right)^{2n}.n=1∑∞63n−1(81)2n.
What is the value of ∑n=1∞(12)n(54)2n?\sum_{n=1}^{\infty} \left(\frac{1}{2}\right)^n \left(\frac{5}{4}\right)^{2n}?n=1∑∞(21)n(45)2n?
If mmm is a positive integer such that ∑n=1∞log(1−1(n+5)2)=logmm+1,\sum_{n=1}^{\infty} \log \left(1-\frac{1}{(n+5)^2}\right) = \log \frac{m}{m+1},n=1∑∞log(1−(n+5)21)=logm+1m, what is the value of m?m?m?
What is the value of ∑n=0∞(3n+1−1)(18)n?\sum_{n=0}^{\infty} \left(3 ^{n+1}-1\right) \left(\frac{1}{8}\right)^{n}?n=0∑∞(3n+1−1)(81)n?
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