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Magazine Problem 53
\(49-54\) . Use a graphing calculator to evaluate the sum. $$ \sum_{n=0}^{22}(-1)^{n} 2 n $$
Problem 53
Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. $$ 1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+\cdots $$
Problem 53
\(49-54\) . A partial sum of an arithmetic sequence is given. Find the sum. $$ \sum_{k=0}^{10}(3+0.25 k) $$
Problem 54
\(49-54\) . Use a graphing calculator to evaluate the sum. $$ \sum_{n=1}^{100} \frac{(-1)^{n}}{n} $$
Problem 54
\(49-54\) . A partial sum of an arithmetic sequence is given. Find the sum. $$ \sum_{n=0}^{20}(1-2 n) $$
Problem 54
Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. $$ \frac{2}{5}+\frac{4}{25}+\frac{8}{125}+\cdots $$
Problem 55
\(55-60\) . Write the sum without using sigma notation. $$ \sum_{k=1}^{5} \sqrt{k} $$
Problem 55
Difference in Volumes of Cubes The volume of a cube of side \(x\) inches is given by \(V(x)=x^{3},\) so the volume of a cube of side \(X+2\) inches is given by \(V(x+2)=(x+2)^{3}\) . Use the Binomial Theorem to show that the difference in volume between the larger and smaller cubes is \(6 x^{2}+12 x+8\) cubic inches
Problem 55
Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. $$ 1+\frac{3}{2}+\left(\frac{3}{2}\right)^{2}+\left(\frac{3}{2}\right)^{3}+\cdots $$
Problem 55
Show that a right triangle whose sides are in arithmetic progression is similar to a \(3-4-5\) triangle.
