Решите уравнение: x-1/x + x-2/x + x-3/x + ... + 1/x = 3

The equation can be rewritten as:

(x-1)/x + (x-2)/x + (x-3)/x + ... + 1/x = 3

This is an arithmetic progression. Let n be the number of terms. The terms are (x-1)/x, (x-2)/x, ..., (x-k)/x, ..., 1/x. The numerators are x-1, x-2, ..., 1. The number of terms is n = x-1.

Sum = (1/x) * [ (x-1) + (x-2) + ... + 1 ] = 3

The sum of the first m integers is m(m+1)/2. Here m = x-1.

(1/x) * [ (x-1)(x-1+1)/2 ] = 3

(1/x) * [ (x-1)x/2 ] = 3

(x-1)/2 = 3

x-1 = 6

x = 7