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Example (Continued)

We have

(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.

which implies (2).

Author: Wolfgang Schreiner
Last Modification: November 24, 1999

(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.