An infinite product P = a₁ a₂ a₃ . . , which is denoted is the limit of the sequence of partial products {a₁, a₁ a₂, a₁ a₂ a₃,  . . .}. Assume that a_k > 0 for all k.

a. Show that the infinite product converges (which means its sequence of partial products converges) provided the series converges.

b. Consider the infinite product

Write out the first few terms of the sequence of partial products,

(for example, P₂ = 3/4, P₃ = 2/3). Write out enough terms to determine the value of

c. Use the results of parts (a) and (b) to evaluate the series 

Transcribed Image Text:

По ак k=1 Σ In ak k=1