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Problems for Chapter VII
N
Problems for Chapter VII 75
1. Given that a n converges, prove that a n o(N).
n n 1
−1
2. Given that a n converges and that a n − a n−1 > , prove that
n n
a n → 0.
ε
3. Show that d(n), the number of divisors of n,is O(n ) for every
positive ε.
1
4. In fact, show that d(n) n log log n .
