Analysis

Induction involving x is no different from other types of induction. Just treat x normally and we can still prove it for the general case.

Let

Then for the base case i.e. n = 0 we have

He have established the RHS=LHS and so P₀ is true. Now assume that the statement is true for n.

We must show that it is also true for n + 1. For the RHS we have

And for the LHS we have

Since LHS=RHS P_n+1 is true. The rest follows.

Analysis

so, the result of this question is 1.