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well... one would think at the base case :P

so its obviously having to prove it for n>1

n>=1

so check n=1 , its true , thats the first step done

then assume it is true for n=k , ie that S(k) { the sum of k terms } = k / (k+1)

now , back to the question ,
S(k+1) = k / (k+1) + 1/ (k+1)(k+2)