In discrete mathematics write an informal proof for Prove th

In discrete mathematics write an informal proof for:

Prove that for any positive integer n, there is an integer k such that:

                                                               n < k+ (1/k) < n+ 2.

the proof may not have more than 50 words, with formulas counting as one word. The informal proof should be an arguemnet with complete, grammaticly correct english sentences, and not a formal arguement.

Solution

Lets start with 1

1<k+(1/k)

2<k+(1/k)

..

for k

k<k+(1/k)

(k²-1)/k<k

-1/k<0

Add 1 on bith sides

k-1<k

k>k-1

Therefore > n+2