the sum to n terms of series 1×4+3×7+5×10+.....will be
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the answer must be 75
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1×4 +3×7+5×10+..
=sigma{(2n-1)(3n+1)}
=sigma(6n×n -n -1)
=6sigma(n*n) -sigma(n) -n
=6{n(n+1)(2n+1)/6} - n(n+1)/2 - n
= n(n+1)(2n+1)-n(n+1)/2 -n
=2n^3 +3n^2 +n -n^2/2 -n/2 -n
=2n*n*n -5n*n/2 -n/2
=sigma{(2n-1)(3n+1)}
=sigma(6n×n -n -1)
=6sigma(n*n) -sigma(n) -n
=6{n(n+1)(2n+1)/6} - n(n+1)/2 - n
= n(n+1)(2n+1)-n(n+1)/2 -n
=2n^3 +3n^2 +n -n^2/2 -n/2 -n
=2n*n*n -5n*n/2 -n/2
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