Sign up ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

I tried,

Refine[Sin[k]^2/(k^2 + k + 1) < 1/(k^2), Element[k, Integers]]


It returns unevaluated. I tried converting Sin[x] into Taylor series but it still doesn't evaluate it.Is there some work around for this or is it that I am doing something wrong ?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

Mathematica returns this inequality:

In[1]:= ineq = Sin[k]^2/(k^2 + k + 1) < 1/(k^2);

unevaluated for integer k because it can be true, false or meaningless for different integers.

For positive (real not only integer number) it's true:

In[2]:= Refine[ineq, k > 0]
Out[2]= True

For 0 RHS doesn't exist and e.g. for -2 it's false:

In[3]:= ineq /. k -> -2
Out[3]= False
share|improve this answer
answer is correct, I got my mistake, I didn't mention domain for K. – Rorschach Jun 13 '14 at 5:13

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.