Understanding Partial Sums

What is the first partial sum of a sequence?

• The sum of the first two terms

• The sum of the first three terms

• The first term of the sequence

• The sum of all terms in the sequence

What is the general idea behind partial sums?

• Subtracting terms of a sequence

• Adding terms of a sequence incrementally

• Adding all terms of a sequence

• Multiplying terms of a sequence

In the sequence involving powers of two, what is the pattern for the nth partial sum?

• (2^n - 1) / 2^n

• 2^(n-1) - 1

• 2^n - 1

• (2^n + 1) / 2^n

In the sequence involving powers of two, what is the denominator of the nth partial sum?

• n^2

• n

• 2^(n-1)

• 2^n

How do you find the nth partial sum for the sequence 1 - 1/(n+1)?

• n/(n+1)

• 1/(n+1)

• n/(n-1)

• 1 - 1/n

For the sequence 1 - 1/(n+1), what happens to the terms as n increases?

• They decrease

• They oscillate

• They increase

• They remain constant

In the sequence involving square roots, what is the pattern for the nth partial sum?

• sqrt(n+1) - 1

• 1 - sqrt(n)

• sqrt(n) - 1

• 1 - sqrt(n+1)

In the square root sequence, what is the relationship between the subscript and the term inside the square root?

• The term is equal to the subscript

• The term is twice the subscript

• The term is one more than the subscript

• The term is one less than the subscript

What is the pattern for the nth partial sum in the logarithmic sequence?

• log(n+1)

• log(1/(n+1))

• log(1/n)

• log(n)

In the logarithmic sequence, how are the logs combined?

• By adding their values

• By subtracting their values

• By dividing their inside terms

• By multiplying their inside terms