27. (a) Let p 1. Show that 1 k+1 1 1 S -dx (k + 1)P...

 

 

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27. (a) Let p 1. Show that 1 k+1 1 1 S -dx (k + 1)P xP kp k for every positive integer k. Hence show that n+1 n+1 dx k=2 xP n k=1 1 kp for every positive integer n. (b) Using the result from (a), show that for every positive integer n, we have (i) n k=1 k In(n + 1), and (ii) n k=1 k2 27. (a) Let p 1. Show that 1 k+1 1 1 S -dx (k + 1)P xP kp k for every positive integer k. Hence show that n+1 n+1 dx k=2 xP n k=1 1 kp for every positive integer n. (b) Using the result from (a), show that for every positive integer n, we have (i) n k=1 k In(n + 1), and (ii) n k=1 k2