See the attached file for questioins

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1. Evaluate

image1.emf

1 4ii=0

∞

∑

1

4

i

i=0

¥

å

2. Using the proof of induction to prove

image2.emf

i2 i=1

N

∑ =1+ 22 + ...+ N2 = N N +1( ) 2N +1( )6

i

2

i=1

N

å

=1+2

2

+...+N

2

=

NN+1

()

2N+1

()

6

is valid for all integers N ≥ 1.

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