If b(0)=1 and b(n)=2*b(n-1), if n is odd and b(n)=b(n-1) if n is even. Find the value of b(100)-b(97)-b(96).


Others by Karthik on 14-Jan-2017 10:53

If b(0)=1 and b(n)=2*b(n-1), if n is odd and b(n)=b(n-1) if n is even. Find the value of b(100)-b(97)-b(96).

Karthik on 13-Apr-2014 18:25Accepted Solution
Ans: 2^48
b(1) = 2*b(1-1) = 2*1 =  2
b(2) = b(1) = 2
b(3) = 2*b(2) = 2*2 = 4
b(4) = b(3) = 4
b(5) = 2*4 = 8
b(6) = 8
Hence b(100)-b(97)-b(96) = 2^50 - 2^49 - 2^48
= 2^48 (4-2-1) = 2^48
SIVARANJANI on 15-Jul-2014 22:59
how to find the last step???
2^48(4-2-1)=2^48

GUNASEELAN on 20-Jul-2014 15:53
b(100)-b(97)-b(96)

b(n)=2*b(n-1)
b(n)=b(n-1)
b(n)=2*b(n)

b(1)=b(2)=2^1
b(3)=b(4)=2^2

b(100)=2^50,  b(100)=b(99)
b(97)=2^49, b(98)=b(97)
b(96)=2^48, b(96)=b(95)

Subashini.R on 25-Aug-2014 17:42
how to find that b(100)-b(97)-b(96)=2^50-2^49-2^48???
TAMOGHNA MAITRA on 12-Apr-2016 11:16
The general formula comes to be for even number (n), b(n)= 2^(n/2) and for odd number, b(n)=2^((n+1)/2)
BALAJI R on 24-Sep-2016 10:25
Ans: 2^48
b(1) = 2*b(1-1) = 2*1 =  2
b(2) = b(1) = 2
b(3) = 2*b(2) = 2*2 = 4
b(4) = b(3) = 4
b(5) = 2*4 = 8
b(6) = 8
Hence b(100)-b(97)-b(96) = 2^50 - 2^49 - 2^48
= 2^48 (4-2-1) = 2^48
Solution
Ans: 2^48
b(1) = 2*b(1-1) = 2*1 =  2
b(2) = b(1) = 2
b(3) = 2*b(2) = 2*2 = 4
b(4) = b(3) = 4
b(5) = 2*4 = 8
b(6) = 8
Hence b(100)-b(97)-b(96) = 2^50 - 2^49 - 2^48
= 2^48 (4-2-1) = 2^48