Question 1

Write the given series in summation notation. $2 - 4 + 8 - 16 + 32 - 64 + 128$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 7 } 4 ^ { i } ( - 1 ) ^ { i }$ 
B)  $\sum _ { i = 1 } ^ { 7 } 4 ^ { i } ( - 1 ) ^ { i + 1 }$ 
C)  $\sum _ { i = 1 } ^ { 7 } 2 ^ { i } ( - 1 ) ^ { i + 1 }$ 
D)  $\sum _ { i = 1 } ^ { 7 } 2 ^ { i } ( - 1 ) ^ { i }$ 
E)  $\sum _ { i = 1 } ^ { 7 } 3 ^ { i } ( - 1 ) ^ { i }$ 
A)  $\sum _ { i = 1 } ^ { 7 } 4 ^ { i } ( - 1 ) ^ { i }$ 
B)  $\sum _ { i = 1 } ^ { 7 } 4 ^ { i } ( - 1 ) ^ { i + 1 }$ 
C)  $\sum _ { i = 1 } ^ { 7 } 2 ^ { i } ( - 1 ) ^ { i + 1 }$ 
D)  $\sum _ { i = 1 } ^ { 7 } 2 ^ { i } ( - 1 ) ^ { i }$ 
E)  $\sum _ { i = 1 } ^ { 7 } 3 ^ { i } ( - 1 ) ^ { i }$

Question 2

Test the series $\sum _ { n = 1 } ^ { \infty } n ( 1.3 ) ^ { n }$ for convergence or divergence using any appropriate test.

Accepted Answer

A) diverges 
B) converges 
A) diverges 
B) converges

Question 3

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) $$- 5 - \frac { 2 } { 1 } , - 5 - \frac { 2 } { 2 } , - 5 - \frac { 2 } { 3 } , - 5 - \frac { 2 } { 4 } , - 5 - \frac { 2 } { 5 } ,$$

Accepted Answer

A)  $a _ { n } = - 5 - \frac { n } { 2 }$ 
B)  $a _ { n } = 2 - \frac { - 5 } { n }$ 
C)  $a _ { n } = 2 - \frac { n } { - 5 }$ 
D)  $a _ { n } = - 5 - \frac { 2 } { n }$ 
E)  $a _ { n } = - 5 - \frac { 2 } { n + 1 }$ 
A)  $a _ { n } = - 5 - \frac { n } { 2 }$ 
B)  $a _ { n } = 2 - \frac { - 5 } { n }$ 
C)  $a _ { n } = 2 - \frac { n } { - 5 }$ 
D)  $a _ { n } = - 5 - \frac { 2 } { n }$ 
E)  $a _ { n } = - 5 - \frac { 2 } { n + 1 }$

Question 4

Complete two iterations of Newton´s Method for the function $f ( x ) = x ^ { 2 } - 10$ using the initial guess 3.1.

Accepted Answer

A) 3.163013, 3.162078 
B) 3.163043, 3.162478 
C) 3.163043, 3.162378 
D) 3.162903, 3.162278 
E) 3.162693, 3.162178 
A) 3.163013, 3.162078 
B) 3.163043, 3.162478 
C) 3.163043, 3.162378 
D) 3.162903, 3.162278 
E) 3.162693, 3.162178

Question 5

Find the indicated term of the sequence. $$\begin{array} { l } 
a _ { n } = ( - 1 ) ^ { n } ( 3 n - 1 ) \
a _ { 16 } = \square
\end{array}$$

Accepted Answer

A) -44 
B) 47 
C) 49 
D) -2 
E) 45 
A) -44 
B) 47 
C) 49 
D) -2 
E) 45

Question 6

The annual profit $a _ { n }$ (in millions of dollars) for a certain company from 2000 to 2005 can be approximated by the model $a _ { n } = 302.58 e ^ { 0.196 n },$ $n = 0,1 , K , 5$ where $n$ represents the year, with $n = 0$ corresponding to 2000. Use the formula for the sum of a finite geometric sequence to approximate the total profit earned during this six-year period. Round to the nearest ten-thousand dollars.

Accepted Answer

A) $3810.36 million 
B) $4112.94 million 
C) $3132.16 million 
D) $2829.58 million 
E) $2325.95 million 
A) $3810.36 million 
B) $4112.94 million 
C) $3132.16 million 
D) $2829.58 million 
E) $2325.95 million

Question 7

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { n }$

Accepted Answer

A)  $- \frac { 8 } { 3 }$ 
B)  $\frac { 8 } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $- \frac { 4 } { 3 }$ 
E) undefined 
A)  $- \frac { 8 } { 3 }$ 
B)  $\frac { 8 } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $- \frac { 4 } { 3 }$ 
E) undefined

Write the given series in summation notation. $2 - 4 + 8 - 16 + 32 - 64 + 128$

Test the series $\sum _ { n = 1 } ^ { \infty } n ( 1.3 ) ^ { n }$ for convergence or divergence using any appropriate test.

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) $- 5 - \frac { 2 } { 1 } , - 5 - \frac { 2 } { 2 } , - 5 - \frac { 2 } { 3 } , - 5 - \frac { 2 } { 4 } , - 5 - \frac { 2 } { 5 } ,$

Complete two iterations of Newton´s Method for the function $f ( x ) = x ^ { 2 } - 10$ using the initial guess 3.1.

Find the indicated term of the sequence. =(-1(3n-1) =\square

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { n }$

Fundamental Concepts of Algebra

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Exam 16: Series and Taylor Polynomials Web

Write the given series in summation notation. 2−4+8−16+32−64+1282 - 4 + 8 - 16 + 32 - 64 + 1282−4+8−16+32−64+128

Test the series ∑n=1∞n(1.3)n\sum _ { n = 1 } ^ { \infty } n ( 1.3 ) ^ { n }∑n=1∞​n(1.3)n for convergence or divergence using any appropriate test.

Complete two iterations of Newton´s Method for the function f(x)=x2−10f ( x ) = x ^ { 2 } - 10f(x)=x2−10 using the initial guess 3.1.

Find the indicated term of the sequence. =(-1(3n-1) =\square

Find the sum of the infinite geometric series. ∑n=0∞4(−12)n\sum _ { n = 0 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { n }∑n=0∞​4(−21​)n

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Probability Web

Filters

Write the given series in summation notation. $2 - 4 + 8 - 16 + 32 - 64 + 128$

Test the series $\sum _ { n = 1 } ^ { \infty } n ( 1.3 ) ^ { n }$ for convergence or divergence using any appropriate test.

Complete two iterations of Newton´s Method for the function $f ( x ) = x ^ { 2 } - 10$ using the initial guess 3.1.

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { n }$