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We have

which implies (2).

( sum_{1 <= i <= n+1}i)= (definition ( sum_{}))( sum_{1 <= i <= n}i) + (n+1)= (1) ( n+1)n/2 + (n+1)= ( n+1)n+2(n+1)/2= ( n+1)(n+2)/2= ( n+1)((n+1)+1)/2.

Author: Wolfgang Schreiner

Last Modification: November 24, 1999