Sequence Math Example 1

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Example 1

easy
Write the first five terms of the sequence an=nn+1a_n = \frac{n}{n+1} for n=1,2,3,…n = 1, 2, 3, \ldots

Solution

  1. 1
    a1=12a_1 = \frac{1}{2}.
  2. 2
    a2=23a_2 = \frac{2}{3}.
  3. 3
    a3=34a_3 = \frac{3}{4}.
  4. 4
    a4=45a_4 = \frac{4}{5}.
  5. 5
    a5=56a_5 = \frac{5}{6}.

Answer

12,  23,  34,  45,  56\frac{1}{2},\; \frac{2}{3},\; \frac{3}{4},\; \frac{4}{5},\; \frac{5}{6}
Each term is found by substituting nn into the formula. The terms increase and approach 1, illustrating that this sequence converges to 1 as n→∞n \to \infty.

About Sequence

An ordered list of numbers generated by a rule, where each number has a specific position (first, second, third, ...).

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More Sequence Examples

Example 2 medium

Determine whether the sequence [formula] converges or diverges. If it converges, find the limit.

Example 3 easy

Write the first four terms of [formula].

Example 4 medium

Determine whether [formula] converges or diverges.

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