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I have posted a link there to this topic so the OP can see my work.Summation of series ( Method of differences )?

Show that r/(r+1)! = 1/r! - 1/(r+1)! , hence or otherwise , evaluate i) sum of r/(r+1)! from 1 to n

ii) sum of (r+2)/(r+1)! from 1 to infinity

giving your answer to part ii in the terms of e .