Review question

# If $f(n) > k$ for all $n \geq 1$, what can we say about $k$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7031

## Suggestion

The inequality $(n+1) + \bigl(n^4+2\bigr) + \bigl(n^9+3\bigr) + \bigl(n^{16}+4\bigr) + \cdots + \bigl(n^{10000}+100\bigr) > k$ is true for all $n\ge 1$. It follows that

1. $k < 1300$,

2. $k^2<101$,

3. $k \ge 101^{10000}$,

4. $k < 5150$.

What happens when $n=1$?

What happens to the LHS when $n=2$? Is it bigger or smaller than for the case $n=1$?