Summit
Prove that the sum from t=0 to m of (-1)^t/t!(m-t)! is zero.
Age
16 to 18
Challenge level
Problem
Prove that the sum
Getting Started
Think about the binomial theorem.
Student Solutions
This neat solution came from Marcos and the result was also
proved by Yatir Halevi:
By the binomial expansion:
This can be proved by induction on $m$ but I won't clutter
this with unnecessary proofs.
Putting in $x= -1$ we have
Dividing through by $m!$ gives us the required
result: