Looks right. Might be better to write it as a sum over an index, i.e. using Σ.nmego12345 said:Homework Statement
Expand x(k+1)/(k+1) - (x-1)(k+1)/(k+1)
Homework Equations
(a+b)m = am + mam - 1b + (mℂ2)am - 2b2 + ... + bm[/B]
The Attempt at a Solution
Here is my solution, I would like to know if it's correct or not
I have the solution in an attached image
The formula for this expression is (x^(k+1) - (x-1)^(k+1))/(k+1).
To expand x^(k+1), you can use the binomial theorem or the power rule for exponents. To expand (x-1)^(k+1), you can use the binomial theorem or the power rule, as well as the fact that (x-1)^k has the same expansion as x^k with alternating positive and negative coefficients.
Expanding this expression can be useful in solving integration problems or simplifying algebraic expressions.
Yes, it can be simplified further by combining like terms and factoring out common factors.
Yes, for this expression to be valid, k must be a positive integer and x cannot be equal to 0 or 1. Additionally, depending on the context, there may be other restrictions on the values of x and k.