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Math Problems
Algebra 2
Convergent and divergent geometric series
Does the infinite geometric series converge or diverge?
\newline
1
+
6
5
+
36
25
+
216
125
+
…
1 + \frac{6}{5} + \frac{36}{25} + \frac{216}{125} + \dots
1
+
5
6
+
25
36
+
125
216
+
…
\newline
Choices:
\newline
(A)converge
\newline
(B)diverge
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Does the infinite geometric series converge or diverge?
\newline
1
+
13
5
+
169
25
+
2
,
197
125
+
…
1 + \frac{13}{5} + \frac{169}{25} + \frac{2,197}{125} + \ldots
1
+
5
13
+
25
169
+
125
2
,
197
+
…
\newline
Choices:
\newline
(A)converge
\newline
(B)diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
6
+
36
+
216
+
…
1 + 6 + 36 + 216 + \ldots
1
+
6
+
36
+
216
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
3
2
+
9
4
+
27
8
+
…
1 + \frac{3}{2} + \frac{9}{4} + \frac{27}{8} + \ldots
1
+
2
3
+
4
9
+
8
27
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
\newline
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
5
3
+
25
9
+
125
27
+
…
1 + \frac{5}{3} + \frac{25}{9} + \frac{125}{27} + \ldots
1
+
3
5
+
9
25
+
27
125
+
…
\newline
Choices:
\newline
(A)converge
\newline
(B)diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
12
5
+
144
25
+
1
,
728
125
+
…
1 + \frac{12}{5} + \frac{144}{25} + \frac{1,728}{125} + \dots
1
+
5
12
+
25
144
+
125
1
,
728
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
4
5
+
16
25
+
64
125
+
…
1 + \frac{4}{5} + \frac{16}{25} + \frac{64}{125} + \ldots
1
+
5
4
+
25
16
+
125
64
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
8
5
+
64
25
+
512
125
+
…
1 + \frac{8}{5} + \frac{64}{25} + \frac{512}{125} + \dots
1
+
5
8
+
25
64
+
125
512
+
…
\newline
Choices:
\newline
(A)converge
\newline
(B)diverge
\newline
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
5
2
+
25
4
+
125
8
+
…
1 + \frac{5}{2} + \frac{25}{4} + \frac{125}{8} + \ldots
1
+
2
5
+
4
25
+
8
125
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
2
+
4
+
8
+
…
1 + 2 + 4 + 8 + \ldots
1
+
2
+
4
+
8
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
7
5
+
49
25
+
343
125
+
…
1 + \frac{7}{5} + \frac{49}{25} + \frac{343}{125} + \ldots
1
+
5
7
+
25
49
+
125
343
+
…
\newline
Choices:
\newline
(A)converge
\newline
(B)diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
8
3
+
64
9
+
512
27
+
…
1 + \frac{8}{3} + \frac{64}{9} + \frac{512}{27} + \dots
1
+
3
8
+
9
64
+
27
512
+
…
\newline
Choices:
\newline
(A)converge
\newline
(B)diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
9
4
+
81
16
+
729
64
+
…
1 + \frac{9}{4} + \frac{81}{16} + \frac{729}{64} + \ldots
1
+
4
9
+
16
81
+
64
729
+
…
\newline
Choices:
\newline
(A)converge
\newline
(B)diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
7
3
+
49
9
+
343
27
+
…
1 + \frac{7}{3} + \frac{49}{9} + \frac{343}{27} + \ldots
1
+
3
7
+
9
49
+
27
343
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
5
+
25
+
125
+
…
1 + 5 + 25 + 125 + \dots
1
+
5
+
25
+
125
+
…
\newline
Choices:
\newline
(A) converge
\newline
(B) diverge
Get tutor help
Click and drag like terms onto each other to simplify fully.
\newline
−
3
−
y
−
1
−
5
x
−
2
+
4
x
-3-y-1-5 x-2+4 x
−
3
−
y
−
1
−
5
x
−
2
+
4
x
Get tutor help
Consider this matrix transformation:
\newline
[
−
1
0
0
−
1
]
\left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right]
[
−
1
0
0
−
1
]
\newline
What is the geometric effect of this transformation?
\newline
Choose
1
1
1
answer:
\newline
(A) A reflection across the
y
y
y
axis
\newline
(B) A reflection across the line
y
=
x
y=x
y
=
x
\newline
(C) A rotation about the origin by
9
0
∘
90^{\circ}
9
0
∘
\newline
(D) A rotation about the origin by
18
0
∘
180^{\circ}
18
0
∘
Get tutor help
Consider this matrix transformation:
\newline
[
−
1
0
0
1
]
\left[\begin{array}{cc} -1 & 0 \\ 0 & 1 \end{array}\right]
[
−
1
0
0
1
]
\newline
What is the geometric effect of this transformation?
\newline
Choose
1
1
1
answer:
\newline
(A) A reflection across the
y
y
y
axis
\newline
(B) A reflection across the line
y
=
x
y=x
y
=
x
\newline
(C) A rotation about the origin by
9
0
∘
90^{\circ}
9
0
∘
\newline
(D) A rotation about the origin by
18
0
∘
180^{\circ}
18
0
∘
Get tutor help
Consider this matrix transformation:
\newline
[
0
1
1
0
]
\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]
[
0
1
1
0
]
\newline
What is the geometric effect of this transformation?
\newline
Choose
1
1
1
answer:
\newline
(A) A reflection across the
y
y
y
axis
\newline
(B) A reflection across the line
y
=
x
y=x
y
=
x
\newline
(C) A rotation about the origin by
9
0
∘
90^{\circ}
9
0
∘
\newline
(D) A rotation about the origin by
18
0
∘
180^{\circ}
18
0
∘
Get tutor help
Consider this matrix transformation:
\newline
[
0
−
1
1
0
]
\left[\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right]
[
0
1
−
1
0
]
\newline
What is the geometric effect of this transformation?
\newline
Choose
1
1
1
answer:
\newline
(A) A reflection across the
y
y
y
axis
\newline
(B) A reflection across the line
y
=
x
y=x
y
=
x
\newline
(C) A rotation about the origin by
9
0
∘
90^{\circ}
9
0
∘
\newline
(D) A rotation about the origin by
18
0
∘
180^{\circ}
18
0
∘
Get tutor help
Does the infinite geometric series converge or diverge?
\newline
1
+
3
4
+
9
16
+
27
64
+
⋯
1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots
1
+
4
3
+
16
9
+
64
27
+
⋯
\newline
Choices:
\newline
[A]converge
\text{[A]converge}
[A]converge
\newline
[B]diverge
\text{[B]diverge}
[B]diverge
Get tutor help
