If for any series b(n)=2b(n-1) when b(n) is odd number and b(n)=b(n-1) if b(n) is even number. then find value of b(100)-b(97)-b(96) if b(0)=1

• 2^48.
  b(100)=b(99)=2b(98)=2b(97)................(1)
  so b(100)-b(97)-b(96)= b(97)-b(96) = 2b(96)-b(96)=b(96)
  
  Now 96 is even so b(96)=b(95)....
  b(95)=(2^1) * b(94)=(2^1) * b(93) =(2^2)* b(91)=(2^3)*b(89)
  
  so here we can realize that 95-2(x) will have 2^x in multiply.... so finally 95-2x=1 => x=47
  
  so finally it will be (2^47) * b(1)=(2^47) * (2)b(0) =2^48 !!!!!!!!!!!! :) I hope this is the answer in given options. right ankit?
  
  
• 9 years agoHelpfull: Yes(20) No(4)
• answer is 2^48
  
  b(100)=b(99)=2^1(b98)=2^1b(97)=2^2b(96)=2^2b(95) ....
  so we can write it as 2^(number of odd numbers starting from 1 to 100)
  no. of odd numbers = 100/2 = 50
  so, b(100)=2^50
  
  simillarly ,
  b(97) = 2^(97/2 + 1) =2^49
  b(96) = 2^(96/2)=2^48
  
  therefore b(100) - b(97) - b(96)
  = 2^50 - 2^49 -2^48
  = 2^48(2^2 - 2 - 1)
  =2^48
  
  
• 9 years agoHelpfull: Yes(10) No(0)
• 2^48 b(0)=2^48
• 9 years agoHelpfull: Yes(3) No(2)
• b(96)=2^48
• 9 years agoHelpfull: Yes(3) No(2)
• we can simple take it like b(100)=2^50 as per given equation and b(97)=2^49 and b(96)=b(95)=2^48
  thn (2^50 - 2^49) = 2^49
  
  nd now 2^49 -2^48= 2^48
  
  so 2^48 is requires answer
  
• 9 years agoHelpfull: Yes(3) No(1)
• b(0)=1
  b(1)=2(b(0))=2*1=2
  b(2)=b(2-1)=b(1)=2
  b(3)=2(b(3-1)=2(b(2))=2(2)=4
  .
  .
  .
  .
  b(100)=b(99)
  b(99)=2b(98)
  b(98)=b(97)
  b(97)=2b(96)
  b(96)=b(95)
  ================b(100)-b(97)-b(96)==>4b(95)-2b(95)-b(95)==>b(95)
  b(95)=2b(94)
  b(95)==96
  ANS:- 96
• 9 years agoHelpfull: Yes(2) No(1)
• b(100)-b(97)-b(96)
  =b(99)-2b(96)-(95)
  =2b(98)-2b(95)-2b(94)
  
  since ,2 is eing multiplied whenver odd to even conversion takes place inside b().
  so count no of even between 2 to 98 =49
  so ,no of 2's will be 2^49 for b(100).
  
  similarly ,for 2^48 for b(97),and 2^47 for b(96)
  
  now solve it
  2^49-2^48-2^47
  =2^47(4-2-1)
  =2^47
• 9 years agoHelpfull: Yes(1) No(3)
• question is wrong since it should be like "n is even or n is odd not b(n))"
• 9 years agoHelpfull: Yes(1) No(0)