Question: 5.6 If x and y are sequences and c E R, we define (cx) k = Cock and (x + y) k = ck +

5.6 If x and y are sequences and c E R, we define (cx) k = Cock and (x + y) k = ck + yk. Prove: If x and y are summable, then a) x + y is summable and OO OO OO [(Ik tyk) = _ yk . k=1 k=1 k=1 b) ex is summable and [ CCK = c Z Ck . k=1 k=1 We note that this exercise shows that the family of summable sequences is a vector space

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