Consider an infinite GP with first term 1,2,3,…,n and common ratios 21​,31​,41​,…,n+11​.∴S1​S2​​=1−1/21​=2=1−1/32​=3⋮⋮​∴​S2n−1​=1−1/2n2n−1​=2nS12​+S22​+S32​+…+S2n−12​​=22+32+42+…+(2n)2=61​(2n)(2n+1)(4n+1)−1​