what will be the value of n in the expression (x/y)^n-2=(y/x)^n-5
Answers
Answer:
xn−yn=(x−y)(xn−1+xn−2y+…+xyn−2+yn−1).
This problem is driving me crazy.
xn−yn=(x−y)(xn−1+xn−2y+⋯+xyn−2+yn−1)
(xn−yn)/(x−y)= the sum for the first n numbers and then I added (xy(n+1)−2+y(n+1)−1) which should equal (xn+1−yn+1)/(x−y) but I can't figure it out
This is a similar problem in the book and I tried this method but it wasn't working out
Thereom 1-2: If x is any real number other than 1, then
∑j=0n−1xj=1+x+x2+…+xn−1=xn−1x−1.
Remark: ∑j=0n−1Aj is shorthand for A0+A1+A2+…+An−1.
Proof: Again we proceed by mathematical induction. If n=1 then ∑j=01−1xj=x0=1 and (x−1)/(x−1)=1. Thus the theorem is true for n=1.
Assuming that ∑j=0k−1xj=(xk−1)/(x−1), we find that
∑j=0(k+1)−1xj=∑j=0k−1xj+xk=xk−1x−1+xk=xk−1+xk+1−xkx−1=xk+1−1x−1.
Hence condition (ii) is fulfilled, and we have established the theorem.
Corollary 1-1: If m and n are positive integers and if m>1, then n<mn.
Answer:
Step-by-step explanation:
