Question

Find an explicit formula for the following sequence, an which starts with a1=−1. −1,1/2,−1/3,1/4,−1/5,…

Answer 1

The sequence can be represented by the formula of its nth term:

`a_n=((-1)^n)/(n)`

Explanation:

Notice that we are in the presence of an alternate sequence (the values alternate from negative to positive. Therefore we need to take into account that there should be a factor "-1" raised to the "n" value for the sequence. Also, given that the sequence looks in absolute value like the harmonic sequence, we conclude upon the following general form for the "nth" term of the sequence:

`a_n=((-1)^n)/(n)`