1 Answer | Add Yours
You need to test if the given sequence is strictly increasing or decreasing, hence, you need to evaluate the difference of two consecutive members of the sequence, such that:
`a_(n+1) - a_n = (n+1)^2 - (n+1) - n^2 + n`
Raising to square yields:
`a_(n+1) - a_n = n^2 + 2n + 1 - n - 1 - n^2 + n`
Reducing dupliuacte members yields:
`a_(n+1) - a_n = 2n`
Since `n>=1` yields that `2n >= 2 > 0` , hence` a_(n+1) - a_n > 0` .
Hence, testing if the given sequence strictly increases or decreases yields that `a_(n+1) - a_n > 0 => a_(n+1) > a_n` , thus the sequence strictly increases.
We’ve answered 315,685 questions. We can answer yours, too.Ask a question