91Ó°ÊÓ

Finding a Formula for a Sum In Exercises \(41-44\) , use mathematical induction to find a formula for the sum of the first \(n\) terms of the sequence. $$\frac{1}{2 \cdot 3}, \frac{1}{3 \cdot 4}, \frac{1}{4 \cdot 5}, \frac{1}{5 \cdot 6}, \ldots, \frac{1}{(n+1)(n+2)}, \dots$$

Finding a Term of a Geometric Sequence, find the indicated term of the geometric sequence. Ist term: \(a_{2}=3, a_{5}=\frac{3}{64}\)

Using a Recursion Formula In Exercises \(43 - 46\) , the first two terms of the arithmetic sequence are given. Find the missing term. $$a _ { 1 } = 3 , a _ { 2 } = 13 , a _ { 9 } =$$

Finding the \(n\) th Term of a Sequence In Exercises \(37-48,\) write an expression for the apparent \(n\) th term \(\left(a_{n}\right)\) of the sequence. (Assume that \(n\) begins with \(1 . )\) $$ 1,-1,1,-1,1, \ldots $$

In Exercises 43-46, find the number of distinguishable permutations of the group of letters. A, L, G, E, B, R, A

Using a Recursion Formula In Exercises \(43 - 46\) , the first two terms of the arithmetic sequence are given. Find the missing term. $$ a _ { 1 } = 4.2 , a _ { 2 } = 6.6 , a _ { 7 } = $$

Finding a Term in a Binomial Expansion In Exercises \(45-52,\) find the specified \(n\) th term in the expansion of the binomial. $$(x+y)^{10}, \quad n=4$$

Finding a Sum In Exercises \(45-54\) , find the sum using the formulas for the sums of powers of integers. $$\sum_{n=1}^{15} n$$

The sample spaces are large and you should use the counting principles discussed in Section 9.6. You draw one card at random from a standard deck of 52 playing cards. Find the probability that (a) the card is an even-numbered card, (b) the card is a heart or a diamond, and (c) the card is a nine or a face card.?

Finding a Term of a Geometric Sequence, find the indicated term of the geometric sequence. 6th term: \(a_{4}=-18, a_{7}=\frac{2}{3}\)