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Is there a way to prove
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}=1-\frac{1}{{n+1)!}
without induction and using only combinatorial arguments?
Induction proof wasn't quite as pleasing for me.
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}=1-\frac{1}{{n+1)!}
without induction and using only combinatorial arguments?
Induction proof wasn't quite as pleasing for me.
This post has been edited 1 time. Last edited by MathBot101101, Apr 21, 2025, 6:45 AM
Reason: im dum
Reason: im dum