10 raise to 2n-1 +1 is divisible by 11

1.	10 raise to 2n-1 +1 is divisible by 11
Answer» 10^(2n-1) +1 is divisible by 11. We will prove this statement by induction. For n = 1 this is true,Now we assume that it is true for n = kTherefore 10^(2k-1) + 1 = 11×t (where t is some integer.=> 10^(2k-1) = 11×t - 1 ..... equation 1For n = k + 1LHS = 10^(2(k+1) - 1) +1 = 100×10^(2k-1) +1 From equation 1 we substitute value of 10^(2k-1),LHS = 100×(11×t - 1) +1= 11 (100×t + 9) which is clearly a multiple of 11.Hence proved

Discussion