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10 raise to 2n-1 +1 is …

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

Posted by Aditi Singh 5 years, 2 months ago

CBSE > Class 11 > Mathematics

1 answers

N Kansara 5 years, 2 months ago

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 = k Therefore 10^(2k-1) + 1 = 11×t (where t is some integer. => 10^(2k-1) = 11×t - 1 ..... equation 1 For n = k + 1 LHS = 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

1Thank You

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