Frequently Use Formula Sum First N Positive Integers Less Commonly Used Formula Sum Square Q37083177

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We frequently use the formula for the sum of the firstn positive integers. Less commonly used is the formula forthe sum of the squares of the first n positiveintegers:

i2 = n(n + 1)(2n + 1)/6

Prove by induction that this formula is correct for n ≥1.

i2 = n(n + 1)(2n + 1)/6 Show transcribed image text i2 = n(n + 1)(2n + 1)/6

Solution

for n=1:———–LHS = 1^2 = 1RHS = 1(1+1)(2+1)/6 = 2*3/6 = 6/6 = 1so, LHS=RHS for n=1let’s assume LHS=RHS for n=kso, 1^2 + 2^2 + … + k^2 = k(k+1)(2k+1)/6for n=k+1:———–LHS = 1^2

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