2. Consider the following sequence of closed subintervals of [0, 1]: | 0, 2 1 3 3 and denote the nth 2 4 subinterval by I,. Now define a sequence of functions f, (x) on [0,1] by [1 fn(x) =- for x in I, for x not in Ip. (a) Show that the sequence {f„(x)} converges in the mean to the zero function on the interval [0, 1]. (b) Show that the sequence {f„(x)} does not converge pointwise at any point of the interval [0, 1].

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.