[" For all "n in N" ,prove by mathematical induction that "],[qquad a+ar+ar^(2)+...+ar^(n-1)=a*(1-r^(n))/(1-r),r!=1]

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

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

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .