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If Sk=(1+2+.....+k)/k , find the value o...

If `S_k=(1+2+.....+k)/k ,` find the value of `S_1^2+S2^2+....+S_n^2dot`

Text Solution

Verified by Experts

Given,
`S_k=(1+2+k)/k`
`s_k=(k(k+1))/(2k)`
`s_k=(k+1)/2`
Now,
`S_1^2+S_2^2+...+S_n^2dot`
`=>((1+1)^2)/4+((2+2)^2)/4+((3+3)^2)/4+...+((n+n)^2)/4`
`=>(2^2+3^2+4^2+...+n^2)/4`
...
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