Solution
= Solution
For each fixed positive <integer> $k$, part (i) gives $(f(n)+g(n))^k\leq(2h(n))^k=2^kh(n)^k$. This meets <big O notation> with constant $2^k$ and threshold $1$. \b[True: $(f+g)^k=O(h^k)$ for fixed $k$.] The constant may depend on $k$; no claim uniform in a varying $k$ is required.