4. (10 points) Assume that the functions fn: [0,1] R, n = N, are continuous and...

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4. (10 points) Assume that the functions fn: [0,1] R, n = N, are continuous and that fn(2) n=1 converges uniformly on [0, 1). Show that the series fn(1) n=1 converges. (2) (3) 4. (10 points) Assume that the functions fn: [0,1] R, n = N, are continuous and that fn(2) n=1 converges uniformly on [0, 1). Show that the series fn(1) n=1 converges. (2) (3)