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Verified answer
(sigma (k + 1)²) / (sigma (4i + k)) = 2sigma (k + 1)² = 2 . sigma (4i + k)
(1+1)²+(2+1)²+(3+1)²+(4+1)²+(5+1)² = 2 [(4i+1)+(4i+2)+(4i+3)+(4i+4)+(4i+5)]
2² + 3² + 4² + 5² + 6² = 2 [20i + 15]
4 + 9 + 16 + 25 + 36 = 40i + 30
90 = 40i + 30
60 = 40i
i = 60/40 = 3/2