Asked by Anthony
Solve:
(x-1)/(x)+(x-2)/(x)+(x-3)/(x)+...+(1)/(x)=3;
X belongs to N
(x-1)/(x)+(x-2)/(x)+(x-3)/(x)+...+(1)/(x)=3;
X belongs to N
Answers
Answered by
Damon
3 x = n x - (1+2+3 ...... n)
1+2+3....+n is arithmetic sequence
https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
a = 1 and d = 1
sum = (n/2)(2 + n-1)= (n/2)(1+n)
= .5(n^2+n)
so
3x = nx -.5(n^2+n)
1+2+3....+n is arithmetic sequence
https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
a = 1 and d = 1
sum = (n/2)(2 + n-1)= (n/2)(1+n)
= .5(n^2+n)
so
3x = nx -.5(n^2+n)
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