1. Evaluate
1 4ii=0
∞
∑
1
4
i
i=0
¥
å
2. Using the proof of induction to prove
i2 i=1
N
∑ =1+ 22 + ...+ N2 = N N +1( ) 2N +1( )6
2
i=1
=1+2
+...+N
=
NN+1
()
2N+1
6
is valid for all integers N ≥ 1.