Maharashtra State BoardHSC Science (General) 11th
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Sum to N Terms of Special Series

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notes

find the sum of first n terms of some special series,
i) 1 + 2 + 3 +…    + n (sum of first n natural numbers) 
ii)  `1^2 + 2^2 + 3^2 +… + n^2`(sum of squares of the first n natural numbers) 
Let us take them one by one.
i)  `S_n=1 + 2 + 3 + … + n`, then `S_n = n(n+1)/2`

ii) `S_n =1^2 + 2^2 + 3^2 +… + n^2`


then = `(n(n+1)(2n+1))/6`

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