trying to prove!). Suppose that 0 1, and define Sk = a1 + a2 + ... + ak. Suppose also that L =E1 bn (so the series converges to a sum L.) n=1 (a) Suppose that a, 2 0 for all n. How do we know that the...

Extracted text: trying to prove!). Suppose that 0 < an="">< bn="" for="" all="" n=""> 1, and define Sk = a1 + a2 + ... + ak. Suppose also that L =E1 bn (so the series converges to a sum L.) n=1 (a) Suppose that a, 2 0 for all n. How do we know that the sequence {Sk} is increasing? Show directly that Sk < sk+1="" (b)="" explain="" why="" the="" sequence="" {sk}="" is="" bounded.="" (c)="" explain="" why="" {sk}="" converges.="" what="" relevant="" theorem="" is="" used="" to="" conclude="" this?="" (d)="" what="" does="" the="" fact="" that="" {sk}="" converges="" have="" to="" do="" with="" convergence="" of="" en="1" an?="" (e)="" would="" part="" a)="" be="" true="" if="" an="" values="" could="" be="" any="" real="" numbers="" (so="" positive="" or="" negative)?="" if="" you="" say="" yes,="" then="" support="" your="" claim="" with="" a="" brief="" argument.="" if="" you="" say="" no,="" then="" give="" a="" counterexample,="" i.e.="" an="" example="" of="" a="" sequence="" {am}="" for="" which="" {s½}="" is="" not="">