How come ( n + 1 n − 1 ) n = ( 1 + 2 n − 1 ) n ?I'm looking at one of my professor's calculus slides and in one of his proofs he uses the identity: ( n + 1 n − 1 ) n = ( 1 + 2 n − 1 ) n Except I don't see why that's the case. I tried different algebraic tricks and couldn't get it to that form.What am I missing?Thanks.Edit: Thanks to everyone who answered. Is there an "I feel stupid" badge? I really should have seen this a mile a way.

Question

How come             (                        n          +          1                          n          −          1                    )        n    =            (      1      +              2                  n          −          1                    )        n  ?I&#039;m looking at one of my professor&#039;s calculus slides and in one of his proofs he uses the identity:            (                        n          +          1                          n          −          1                    )        n    =            (      1      +              2                  n          −          1                    )        n  Except I don&#039;t see why that&#039;s the case. I tried different algebraic tricks and couldn&#039;t get it to that form.What am I missing?Thanks.Edit: Thanks to everyone who answered. Is there an &quot;I feel stupid&quot; badge? I really should have seen this a mile a way.

Terrance Phillips · Accepted Answer

Just write            (                        n          +          1                          n          −          1                    )        n    =            (                        n          −          1          +          2                          n          −          1                    )        n    =            (      1      +              2                  n          −          1                    )        n

Nicholas Cruz · Accepted Answer

Note that            n      +      1              n      −      1        =            n      −      1      +      2              n      −      1        =            n      −      1              n      −      1        +      2          n      −      1        =  1  +      2          n      −      1        .

How come ( n + 1 </mro

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