91Ó°ÊÓ

Finding a Sum In Exercises \(75-78\) , use a graphing utility to find the sum. $$ \sum_{n=0}^{25} \frac{1}{4^{n}} $$

In Exercises \(75-82,\) solve for \(n\) $$_{n+2} P_{3}=6 \cdot_{n+2} P_{1}$$

Sum of an Infinite Geometric Series, find the sum of the infinite geometric series. $$ 9+6+4+\frac{8}{3}+\dots $$

Expanding a Complex Number In Exercises \(73-78\) , use the Binomial Theorem to expand the complex number. Simplify your result. $$(5-\sqrt{3} i)^{4}$$

True or False? In Exercises 77 and 78 , determine whether the statement is true or false. Justify your answer. A sequence with \(n\) terms has \(n-1\) second differences.

Approximation In Exercises \(79-82,\) use the Binomial Theorem to approximate the quantity accurate to three decimal places. For example, in Exercise \(79,\) use the expansion \((1.02)^{8}=(1+0.02)^{8}\) $$=1+8(0.02)+28(0.02)^{2}+\cdots+(0.02)^{8}$$ $$(1.02)^{8}$$

In Exercises \(75-82,\) solve for \(n\) $$14 \cdot_{n} P_{3}=_{n+2} P_{4}$$

Using Sigma Notation to Write a Sum In Exercises \(79-88\) , use sigma notation to write the sum. $$ \frac{1}{3(1)}+\frac{1}{3(2)}+\frac{1}{3(3)}+\dots+\frac{1}{3(9)} $$

Sum of an Infinite Geometric Series, find the sum of the infinite geometric series. $$ \frac{1}{9}-\frac{1}{3}+1-3+\cdots $$

Approximation In Exercises \(79-82,\) use the Binomial Theorem to approximate the quantity accurate to three decimal places. For example, in Exercise \(79,\) use the expansion \((1.02)^{8}=(1+0.02)^{8}\) $$=1+8(0.02)+28(0.02)^{2}+\cdots+(0.02)^{8}$$ $$(2.005)^{10}$$