ECS20
Discussion: 11/10 to 11/16
Induction:
Use induction to prove each of the following:
n
(-1)n n(n +1)
a) å(-1)i i 2 =
for all n >0
2
i=1
b) 2 n £ n!
for all n≥4
n
1
n
c) å
for all n>0
=
n +1
i=1 i(i +1)
Fibonacci:
The following problems refer to the Fibonacci numbers defined in class:
a) Show that for all n >0, f1 + f 2 + + f n = f n +2 -1
b) Show that for all n>0, f4n is divisible by 3.