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Chapter 19: Problem 7
A geometric sequence is given by \(1, \frac{1}{2}, \frac{1}{4}, \ldots\) What is its common ratio?
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(a) Obtain a quadratic Maclaurin polynomial approximation, \(p_{2}(x)\), to \(f(x)=\cos 2 x\). (b) Compare the approximate value given by \(p_{2}(1)\) with actual value \(f(1)\).
The sum to infinity of a geometric sequence is four times the first term. Find the common ratio.
A sequence is given by \(5, \frac{5}{8}, \frac{5}{27}, \frac{5}{64}, \ldots\) Write down an expression to denote the full sequence.
A geometric series has \(S_{3}=\frac{37}{8}\) and \(S_{6}=\frac{3367}{512}\). Find the first term and the common ratio.
Find the sum of the squares of the first 20 positive integers.
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