If [x] denotes greatest integer less than or equal to x, then ([13 x] + [23 x]+.....+[n3 x]) is equa

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If [x] denotes greatest integer less than or equal to x, then ([13 x] + [23 x]+.....+[n3 x]) is equal to

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([13 x] + [23 x]+.....+[n3 x]) 13 x -1 < [13 x] &#8804; 13 x23 x -1 < [23 x] &#8804; 23 x . . . . . . . . .n3 x - 1 < [n3 x] n3 xAdding all these inequilities(13 + 23 + 33 ...........+ n3) x - n < [13x] + [23x] + ...........[n3x] (13 + 23 + ..........n3)x&#8756;

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