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Let a(n) denote the number of all n-digi...

Let `a_(n)` denote the number of all n-digit numbers formed by the digits 0,1 or both such that no consecutive digits in them are 0. Let `b_(n)` be the number of such n-digit integers ending with digit 1 and let `c_(n)` be the number of such n-digit integers ending with digit 0. Which of the following is correct ?

A

`a_(17)=a_(16)+a_(15)`

B

`c_(17)nec_(16)+c_(15)`

C

`b_(17)neb_(16)+c_(16)`

D

`a_(17)=c_(17)+b_(16)`

Text Solution

Verified by Experts

The correct Answer is:
A
by recurring formula `a_(17)=a_(16)+a_(15)` is correct.
also, `C_(17) ne C_(16)+C_(15) impliesa_(15) ne a_(14)+a_(13)` `[becauseC_(n)=a_(n-2)]`
`therefore`Incorrect, similarly, other parts are also incorrect.
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