Question

Sequences: A sequence is of the form a1, a2, a3, a4, ... where the an are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers. Sequences may be defined in various ways: By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is 1/2, 2/5, 3/10, 4/17, 5/26, 6/37, ... Then the n-th term is an = . Explicitly. For example, suppose an = n^n. Then a1 = , a2 = , and a3 = . Recursively. For example, the Fibonacci Sequence is defined by a1 = a2 = 1, an+1 = an + an-1, n = 2, 3, 4, ... Thus a3 = , a4 = , and a5 = . Also a sequence may or may not have a limit. For the following sequences, enter the limit, or enter the letter "D" if the sequence diverges. an = n an = 1/n an = (n^2+4n-5)/((2n-1)(3n-1))

          Sequences: A sequence is of the form
a1, a2, a3, a4, ...
where the an are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers.
Sequences may be defined in various ways:
By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is
1/2, 2/5, 3/10, 4/17, 5/26, 6/37, ...
Then the n-th term is
an = .
Explicitly. For example, suppose an = n^n. Then a1 = , a2 = , and a3 = .
Recursively. For example, the Fibonacci Sequence is defined by
a1 = a2 = 1, an+1 = an + an-1, n = 2, 3, 4, ...
Thus a3 = , a4 = , and a5 = .
Also a sequence may or may not have a limit. For the following sequences, enter the limit, or enter the letter "D" if the sequence diverges.
an = n
an = 1/n
an = (n^2+4n-5)/((2n-1)(3n-1))

Sequences: A sequence is of the form
a1, a2, a3, a4, ...
where the an are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers.
Sequences may be defined in various ways:
By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is
1/2, 2/5, 3/10, 4/17, 5/26, 6/37, ...
Then the n-th term is
an = .
Explicitly. For example, suppose an = n^n. Then a1 = , a2 = , and a3 = .
Recursively. For example, the Fibonacci Sequence is defined by
a1 = a2 = 1, an+1 = an + an-1, n = 2, 3, 4, ...
Thus a3 = , a4 = , and a5 = .
Also a sequence may or may not have a limit. For the following sequences, enter the limit, or enter the letter "D" if the sequence diverges.
an = n
an = 1/n
an = (n^2+4n-5)/((2n-1)(3n-1))

Added by Hugo B.

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