Question: Prove: for every positive integer n, 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n(n+1)) = n/(n+1) Prove: for every integer n, 1+2+3+,,,+n = n(n+1)/2

  1. Prove: for every positive integer n, 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n(n+1)) = n/(n+1)
  2. Prove: for every integer n, 1+2+3+,,,+n = n(n+1)/2
  3. Prove: if a sequence is defined recursively by a1 =1 and an = n/(n-1) an-1 for n> 2 then an=n for every positive integer n

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