Exam 14: Sequences, Series, and the Binomial Theorem

For the given geometric sequence, find the limit of the infinite series, if it exists. - $- 15 , - 5 , - \frac { 5 } { 3 } , - \frac { 5 } { 9 } , \ldots$

Write the sum using summation notation. - $0 + 1 + 2 + 3 + 4$

Solve the problem. -Suppose you invest $9197 at the end of each year into an account earning 8% interest (compounded annually). At the end of 8 years, how much money will be in the account?

Evaluate the given binomial coefficient. - ${ } _ { 9 } \mathrm { C } _ { 4 }$

Solve the problem. -A man earned $3000 the first year he worked. If he received a raise of $500 at the end of each year, what was his salary during the 15th year?

Find the indicated partial sum for the sequence with the given general term. -s5, $a _ { n } = - 5 n - 8$

Find the sum. - $\sum _ { i = 2 } ^ { 5 } \left( i ^ { 2 } - 5 \right)$

Write the sum using summation notation. - $\frac { 1 } { 10 } + \frac { 1 } { 11 } + \frac { 1 } { 12 } + \frac { 1 } { 13 } + \frac { 1 } { 14 }$

Find the general term an of the given sequence. - $- 1,1,3,5,7 , \ldots$

Find the indicated partial sum for the given sequence. - $\mathrm { s } _ { 4 } , 81,243,729,2187 , \ldots$

Find the indicated partial sum for the given geometric sequence. -s4, 16, 32, 64, 128, ...

Find the general term, an, of the given geometric sequence. - $1 , \frac { 1 } { 6 } , \frac { 1 } { 36 } , \ldots$

Find the sum. - $\sum _ { i = 3 } ^ { 6 } \frac { \left( i ^ { 2 } - 3 \right) } { 2 }$

Find the common ratio, r, for the geometric sequence. - $243 , - 81,27 , - 9 , \ldots$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $2 \cdot \left( \frac { 1 } { 2 } \right) ^ { \mathrm { n } - 1 }$

Expand using the binomial theorem. - $( x + 4 ) ^ { 3 }$

Find the common ratio, r, for the geometric sequence. -1

Find the general term, an, of the given geometric sequence. - $1,6,36 , \ldots$

Find the indicated partial sum for the given sequence. - $510 , - 5 , - 51 , - 97 , \ldots$

Find the indicated term for the sequence. -Find the $13 ^ { \text {th } }$ term of the sequence whose general term is $\mathrm { a } _ { \mathrm { n } } = \mathrm { n } ^ { 2 } - \mathrm { n }$ .