Suppose a sequence of reals {an}n≥0 satisfies a0=0, 101100<a100<1, and
2an−an−1−an+1≤2(1−an)3
for every n≥1.
(1) Define a sequence bn=an−n+1n. Prove that bn≤bn+1 for any n≥100.
(2) Determine whether infinite series ∑n=1∞n2an converges or diverges.