For n N, let cn be defined by cn := 1/1 + 1/2 + +1/n - ln

For n ˆˆ N, let cn be defined by cn := 1/1 + 1/2 + ˆ™ ˆ™ ˆ™+1/n - ln n. Show that (cn) is a decreasing sequence of positive numbers. Show that if we put

then the sequence (bn) converges to ln 2. [bn = c2n - cn + ln 2.]

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