Let am, bm be complex numbers and let m-0 am 100 = A, m-0 bm =...

 

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Let am, bm be complex numbers and let m-0 am 100 = A, m-0 bm = B be two convergent sums. Assume m k=0 further that the first sum converges absolutely. Let Cm = K/K-0 am-kbk. Show that m=0 Cm = show that the sequence of partial sums of the cm's converges to AB. AB, i.e. Let am, bm be complex numbers and let m-0 am 100 = A, m-0 bm = B be two convergent sums. Assume m k=0 further that the first sum converges absolutely. Let Cm = K/K-0 am-kbk. Show that m=0 Cm = show that the sequence of partial sums of the cm's converges to AB. AB, i.e.