`a+ar+ar^(2)+...+ar^(n-1)=(a(r^(n)-1))/(r-1)`

a+ar+ar^(2)+...+ar^(n-1)=(a(1-r^(n)))/(1-r) forall n in N.

Statement -1 For all natural numbers n , 0.5+0.55+0.555+...... upto n terms =(5)/(9){n-(1)/(9)(1-(1)/(10^n))} , Statement-2 a+ar+ar^2+....+ar^(n-1)=(a(1-r^n))/((1-r)) , for 0lt r lt 1 .

Statement -1 For all natural numbers n , 0.5+0.55+0.555+...... upto n terms =(5)/(9){n-(1)/(9)(1-(1)/(10^n))} , Statement-2 a+ar+ar^2+....+ar^(n-1)=(a(1-r^n))/((1-r)) , for 0lt r lt 1 .

Statement -1 For all natural numbers n , 0.5+0.55+0.555+...... upto n terms =(5)/(9){n-(1)/(9)(1-(1)/(10^n))} Statement-2 a+ar+ar^2+....+ar^(n-1)=(a(1-r^n))/((1-r)) , for 0lt r lt 1 .

Statement -1 For all natural numbers n , 0.5+0.55+0.555+...... upto n terms =(5)/(9){n-(1)/(9)(1-(1)/(10^n))} Statement-2 a+ar+ar^2+....+ar^(n-1)=(a(1-r^n))/((1-r)) , for 0lt r lt 1 .

Statement -1 For all natural numbers n , 0.5+0.55+0.555+...... upto n terms =(5)/(9){n-(1)/(9)(1-(1)/(10^n))} , Statement-2 a+ar+ar^2+....+ar^(n-1)=(a(1-r^n))/((1-r)) , for 0lt r lt 1 .

Using the principle of finite Mathematical Induction prove the following: (iv) a+ar+ar^(2)+……..+"n terms" = (a(r^(n)-1))/(r-1) , r != 1 .

For all ninNN , prove by principle of mathematical induction that, a+ar+ar^(2)+ . . . to n terms =a*(r^(n)-1)/(r-1)[rne1] .

Prove that the sum of n terms of the reciprocals of the terms of the series a, ar, ar^(2),…" is "(1-r^(n))/(a(1-r)r^(n-1))

Prove that the sum of n terms of the reciprocals of the terms of the series a, ar, ar^(2),…" is "(1-r^(n))/(a(1-r)r^(n-1))