A-1 Bounding summations Give asymptotically tight bounds on the following summations. Assume that r 0 and s 2 0 are constants. a. k

Find a simple formula for Σ 1(2k-1). Show that Σ series. i 1/(2kー1) = ln( n) + 0(1) by man ipulating the harmoni«

Show t( x)/x) for <l<I. Show that Σ000(k-1)/2-0.

Evaluate the sum 2k +l)x2* Prove that Σ-1 OU. (i)) = 0(Σ- summations 1 fk (i)) by using the linearity property of

Evaluate the product Π-2(1-1/k2).

A.2-1 Show that Σ” i 1/k 2 is bounded above by a constant. A.2-2 Ign

A.2-3 Show that the nth harmonic number is 2(lg n) by splitting the summation A.2-4 Approximate Σ-i k 3 with an integral. A.2-5 Why didn’t we use the integral approximation (A12) directly on Σ, 1/k to obtain an upper bound on the nth harmonic number?