Find (a) the fourth partial sum and (b) the sum of the infinite series. $\sum_{k=1}^{\infty} \frac{4}{10^{k}}$

Write the first five terms of the geometric sequence. $a_{1}=\frac{1}{4}, r=7 x$

To find the probability that the sales representative in previous exercise makes four sales if the probability of a sale with any one customer is $\frac{1}{2}$, evaluate the term ${ }_8 C_4\left(\frac{1}{2}\right)^4\left(\frac{1}{2}\right)^4$ in the expansion of $\left(\frac{1}{2}+\frac{1}{2}\right)^8$

Consider n independent trials of an experiment in which each trial has two possible outcomes, success or failure. The probability of a success on each trial is p and the probability of a failure is q = 1 - p. In this context, the term $_{n} C_{k} p^{k} q^{n-k}$ in the expansion of $(p + q)^n$ gives the probability of k successes in the n trials of the experiment. The probability of a sales representative making a sale to any one customer is $\frac{1}{3}$. The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term $_{8} C_{4}\left(\frac{1}{3}\right)^{4}\left(\frac{2}{3}\right)^{4}$ in the expansion of $\left(\frac{1}{3}+\frac{2}{3}\right)^{8}$

Find the indicated partial sum of the series. $\sum_{n=1}^{\infty} 4\left(-\frac{1}{2}\right)^{n}$ Third partial sum

Write the first five terms of the geometric sequence. $a_{1}=3, r=\frac{x}{2}$

Determine whether the statement is true or false. Justify your answer. You can find the nth term of a geometric sequence by multiplying its common ratio by the first term of the sequence raised to the (n − 1)th power.

Consider n independent trials of an experiment in which each trial has two possible outcomes, success or failure. The probability of a success on each trial is p and the probability of a failure is q = 1 - p. In this context, the term $_{n} C_{k} p^{k} q^{n-k}$ in the expansion of $(p+q)^{n}$ gives the probability of k successes in the n trials of the experiment. The probability of a baseball player getting a hit during any given time at bat is $\frac{1}{4}$. To find the probability that the player gets three hits during the next 10 times at bat, evaluate the term $_{10} \mathrm{C}_{3}\left(\frac{1}{4}\right)^{3}\left(\frac{3}{4}\right)^{7}$ in the expansion of $\left(\frac{1}{4}+\frac{3}{4}\right)^{10}$

Find the indicated partial sum of the series. $\sum_{i=1}^{\infty} \frac{2}{3^{i}}$ Fifth partial sum

Determine whether the statement is true or false. Justify your answer. The first n terms of a geometric sequence with a common ratio of 1 are the same as the first n terms of an arithmetic sequence with a common difference of 0 if both sequences have the same first term.

Find the indicated partial sum of the series. $\sum_{i=1}^{\infty} \frac{7}{5^{i}}$ Fourth partial sum

Consider n independent trials of an experiment in which each trial has two possible outcomes, success or failure. The probability of a success on each trial is p and the probability of a failure is q = 1 - p. In this context, the term $_{n} C_{k} p^{k} q^{n-k}$ in the expansion of $(p+q)^{n}$ gives the probability of k successes in the n trials of the experiment. A fair coin is tossed seven times. To find the probability of obtaining four heads, evaluate the term $_{7} C_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{3}$ in the expansion of $\left(\frac{1}{2}+\frac{1}{2}\right)^{7}$.

Determine whether the statement is true or false. Justify your answer. For a geometric sequence in which the quotient of term $a_{7}$ and term $a_{5}$ is 16, the common ratio is 8.

Use sigma notation to write the sum. Then use a graphing utility to find the sum. $\frac{1}{2}+\frac{2}{4}+\frac{6}{8}+\frac{24}{16}+\frac{120}{32}+\frac{720}{64}$