Q. 2

# Prove the followi

Let Assume P(n):12 + 22 + 32 + - - - + n2 = For n = 1

P(1): 1 = 1=1

= P(n) is true for n = 1

Let P(n) is true for n = k, so

P(k): 12 + 22 + 32 + - - - - - + k2 = Let’s check for P(n) = k + 1, So

P(k): 12 + 22 + 32 + - - - - - + k2 + (k + 1)2 = = 12 + 22 + 32 + - - - - - + k2 + (k + 1)2

= = = = = = = Therefore, P(n) is true for n = k + 1

Hence, P(n) is true for all nN by PMI

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