x-1-x-x-2-x-x-3-x-1-x-3-x-Easy-question-

Question Number 153339 by amin96 last updated on 06/Sep/21

\frac{x - 1}{x} + \frac{x - 2}{x} + \frac{x - 3}{x} + \dots + \frac{1}{x} = 3 x = ?

∵∴∵∴∵ E a s y q u e s t i o n ∴∵∴∵∴∵

Answered by MJS_new last updated on 06/Sep/21

\frac{\underset{j = 1}{\sum^{x - 1}} j}{x} = \frac{x - 1}{2} = 3 \Rightarrow x = 7

Answered by talminator2856791 last updated on 06/Sep/21

3 x = (x - 1) + (x - 2) + \dots . . + 1

0 = (- 1) + (- 2) + (- 3) + (x - 4) + \dots . . + 1

0 = - 6 + (x - 4) + \dots . . + 1

6 = (x - 4) + \dots . . + 1

6 = \frac{(x - 4) (x - 3)}{2}

12 = (x - 4) (x - 3)

12 = x^{2} - 7 x + 12

0 = x^{2} - 7 x

0 = x (x - 7)

x = 7