Question
Sun September 06, 2009 By:

what is the sum of the series [x^2 +[x+dx]^2.........[x+n*dx]^2]

Expert Reply
Tue September 08, 2009

x2 +(x+dx)2.........(x+ndx)2 = x2 + (x2+(dx)2 + 2dx) + (x2+(2dx)2 + 4dx) ...........................(x2+(ndx)2 + 2ndx)

                                            = x2 + (x2+dx2+2dx)+ (x2+4dx2+4dx)+ ...................................(x2+(ndx)2 + 2ndx)

                                            = (x2 +x2+ ....................n terms) + dx2 (1+4 + 9........)+ 2dx (1+2+3..........)

                                            = nx2 + (dx2 (n)(n+1)(2n+1))/6  + 2dx (n(n+1)/2)

                                           = nx2 + (dx2 (n)(n+1)(2n+1))/6  + dx (n(n+1)

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