AnswersPrecalculusLimits as They Relate to Sequences and Series

Limits as They Relate to Sequences and Series — Quiz Answers

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Consider the sequence 3 halves comma 4 thirds comma 5 fourths comma 6 fifths comma dot dot dot Which statement describes the sequence?

A
The sequence converges to infinity .
B
The sequence converges to 1 .
C
The sequence diverges.
D
The sequence converges to 0 .
2
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Consider the sequence left divided by 1 comma negative 3 comma 9 comma negative 27 comma 81 comma point point point Which statement describes the sequence?

A
The sequence converges to 1 .
B
The sequence diverges.
C
The sequence converges to infinity .
D
The sequence converges to 0 .
3

Which statement describes the series? the sum from n is equal to 1 to infinity of 4

A
The series converges and it has a sum of 4 .
B
The series converges and it has a sum of 1
C
The series diverges and it does not have a sum.
D
The series diverges and it has a constant ratio of 4.
4

Consider the series 1 eighth plus 1 over 16 plus 1 over 32 plus 1 over 64 plus 1 over 128 plus dot dot dot Which expression defines cap s sub n ?

A
limit n to infinity of the fraction with numerator 2 to the n th power minus 1 and denominator 4 times open paren 2 to the n th power close paren
B
limit n to infinity of the fraction with numerator 1 and denominator 4 times open paren 2 to the n th power close paren
C
limit n to infinity of the fraction with numerator 1 and denominator 2 to the n th power
D
limit n to infinity of the fraction with numerator 2 to the n th power and denominator 4 times open paren 2 to the n th power close paren
5

Which statement describes the sequence defined by A sub n is equal to the fraction with numerator n squared minus 16 and denominator n cubed plus 4 ?

A
The sequence diverges.
B
The sequence converges to 0 .
C
The sequence converges to 1 .
D
The sequence converges to infinity .
6

Which statement describes the sequence defined by A sub n is equal to the fraction with numerator n cubed minus n and denominator n squared plus 5 n ?

A
The sequence converges to 0 .
B
The sequence converges to infinity .
C
The sequence converges to negative infinity .
D
The sequence diverges.
7

Which statement describes the series? the sum from n is equal to 1 to infinity of 3 fourths

A
The series converges and it has a sum of 2 .
B
The series converges and it has a sum of 3 fourths .
C
The series diverges and it does not have a sum.
D
The series diverges and it has a constant ratio of 3 fourths.
8

Which rule defines cap s sub n for A sub n is equal to 3 times 0 point 7 to the n th power ?

A
cap s sub n is equal to 2 point 1 times open paren 1 minus 0 point 7 to the n th power close paren
B
cap s sub n is equal to 7 times open paren 1 minus 0 point 7 to the n th power close paren
C
cap s sub n is equal to 2 point 1 times open paren 0 point 7 to the n th power close paren
D
cap s sub n is equal to 7 times open paren 0 point 7 to the n th power close paren
9

Consider the sequence 1 comma 4 comma 16 comma 64 comma 128 comma point point point Which statement describes the sequence?

A
The sequence converges to negative infinity .
B
The sequence diverges.
C
The sequence converges to 0 .
D
The sequence converges to infinity .
10

Consider the sequence three fourths comma four fifths comma five sixths comma six sevenths comma point point point Which statement describes the sequence?

A
The sequence converges to infinity .
B
The sequence converges to 1 .
C
The sequence converges to negative infinity .
D
The sequence diverges.

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