Using principle of mathematical induction prove that for all nϵN xn-yn is divisible by x-y Share with your friends Share 0 Varun.Rawat answered this Let the given statement be Pn. ThenPn : xn - yn is divisible by x - yPut n = 1P1 : x - y is divisible by x-y which is clearly true.So, P1 is true.Let Pk be true. Then,Pk : xk - yk is divisible by x - y ....1Now, xk+1 - yk+1 = xk+1 - xky + xky - yk+1=xkx - y + yxk - yk , which is divisible by x - y Using 1⇒Pk+1 : xk+1 - yk+1 is divisible by x - y⇒Pk+1 is true when Pk is trueThus, P1 is true and Pk+1 is true whenever Pk is true.Hence, by PMI, Pn is true for all n∈N -1 View Full Answer Saloni answered this If you have R.D Sharma of mathematics then plzz see the page no. 12.11 example no13. It will help you. 1
