(ii) 2^3n – 26n – 1 is divisible by 676, for all n e N.
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Question From class 11 Chapter BINOMIAL THEOREM
It
is a positive integer, prove that
is divisible by
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Text Solution
Solution :
We will prove it using mathematical induction.<br> Given expression is.<br>
<br> When
, given expression is,<br>
<br> So, for
, given expession is divisible by
.<br> Let for any
, given expression is divisible by
.<br> Then,
, where
is a natural number.<br> Now, we have to prove, for
, given expression is divisible by
.<br> For
, given expression is,<br>
<br>
<br> From (1),<br>
<br>
<br>
<br>
<br>
<br>, which is clearly divisible by
.<br> Thus, given expression will be divisible by
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