13. Let x be any positive real number, and define a sequence (an)-1 by [x] +...

  

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13. Let x be any positive real number, and define a sequence (an)-1 by [x] + [2x] + + [mx] n² an where [x] is the largest integer less than or equal to x. Prove that {an)-1 converges to x/2. 13. Let x be any positive real number, and define a sequence (an)-1 by [x] + [2x] + + [mx] n² an where [x] is the largest integer less than or equal to x. Prove that {an)-1 converges to x/2.

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Proof We will use the fact that for any positive integer n we have x 2x nx nxn ... View the full answer