Let P be the statement that 1+2x+3x^2+....+nx^n-1=1-(n+1)x^n+nx^n-1/(1-x)^2
When n=1
L.H.S=1(x)^0=1 R.H.S={1-(1+1)x+x^0}/(1-x)^2=1
Therefore,P is true when n=1
Assume that P is true when n=k
I.e. 1+2x+3x^2+....+kx^n-1=1-(k+1)x^k+kx^k-1/(1-x)^2
When n=k+1
[ omegah4400在2009-12-14 19:32重新編輯此帖 ]