I was asked to prove that is a null sequence, that is, . c is a real number.
I said that the sequence tends to zero if for all n sufficiently large the denominator grows faster than the numerator. If this is true for all n sufficiently large then the denominator is infinitely larger than the numerator in the limit and so the limit is zero.
The numerator grows at the rate and the denominator grows at the rate
For any c there exists n0 such that n+1>c for all n>n0 therefore the sequence is a null sequence.
I got zero marks for this, the lecturer later gave the solution in the image I attached. Maybe he was just being picky but I don't see what is wrong with my proof, could someone please show me where I went wrong if I went wrong?
I see the following problematic places in your proof.