sum of series 2^2+4^2+6^2+.....n^2

Dear Student,
Please find below the solution to the asked query:

S=22+42+62+...+n2a1=21=2×12a2=42=2×22a3=62=2×32...an2=n2=2×n22So, ak=2×k2ak=4k2Now, S=k=1n2ak=k=1n24k2=4k=1n2k2=4n2n2+12n2+16=2n2n+22n+13=2nn+2n+12×2×3 S=nn+1n+26

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