Prove that `a+ar+ar^2+.......+n "terms" =(a(r^n+1))/(r-1),r ne 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] .

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

Prove the following by using the principle of mathematical induction for all n in N :- a + ar + ar^2+...+ ar^(n-1)=(a(r^n-1))/(r-1) .

Prove that by using the principle of mathematical induction for all n in N : a+ ar+ ar^(2)+ ..+ ar^(n-1)= (a(r^(n)-1))/(r-1)

Prove the following by using the principle of mathematical induction for all n in N a+ar + ar^2 +…….+ ar^(n-1) = (a(r^n - 1))/(r - 1)

Prove that by using the principle of mathematical induction for all n in N : a+ ar+ ar^(2)+ ..+ ar^(n-1)= (a(r^(n)-1))/(r-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 .