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Match the following . {:(,"ColumnI",,"...

Match the following .
`{:(,"ColumnI",,"ColumnII"),((i) ,1^(2) +2^(2) +3^(2) +....+n^(2) ,(a) ,[(n(n+1))/(2)]^(2)),((ii) , 1^(3) +2^(3) +3^(3) +...+n^(3) ,(b), n(n+1)),((iii),2+4+6+...+2n,( c),(n(n+1)(2n+1))/(6)),((iv),1+2+3+...+n,(d),(n(n+1))/(2)):}`

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To solve the problem of matching the sums in Column I with their corresponding formulas in Column II, we will analyze each item step by step. ### Step 1: Analyze the first item in Column I **Item (i):** \(1^2 + 2^2 + 3^2 + \ldots + n^2\) The formula for the sum of squares of the first \(n\) natural numbers is given by: \[ \text{Sum} = \frac{n(n+1)(2n+1)}{6} ...
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