What is the sum of the roots of the equation
$$(x − 1) + (x − 2)^2 + (x − 3)^3 + ... + (x − 10)^{10} = 0 $$?
When i expand this equation, it become in the power of 10 and its get complicated. Now what i am thinking is the sum of roots will be equal to the sum of coefficents of x^9
.So i just need to evaluate coefficent of x^9
in the term $$(x-10)x^{10}$$. Am in right in thinking?
But is there is any other easier way by which i can calculate?
Thanks in advance.