# 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).

#### OthersKarthik 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).

on 13-Apr-2014 18:25

Ans: 2^48<br>b(1) = 2*b(1-1) = 2*1 =&nbsp; 2<br>b(2) = b(1) = 2<br>b(3) = 2*b(2) = 2*2 = 4<br>b(4) = b(3) = 4<br>b(5) = 2*4 = 8<br>b(6) = 8<br>Hence b(100)-b(97)-b(96) = 2^50 - 2^49 - 2^48<br>= 2^48 (4-2-1) = 2^48
on 15-Jul-2014 22:59

how to find the last step???<br>2^48(4-2-1)=2^48<br><br>
on 20-Jul-2014 15:53

<span style="font-family: Arial, Helvetica, sans-serif; font-size: 15px; line-height: 22px; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255);">b(100)-b(97)-b(96)</span><div style="font-family: Arial, Verdana; font-size: 10pt; line-height: normal;"><span style="color: rgb(34, 34, 34); font-family: Arial, Helvetica, sans-serif; font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);"><br></span></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(n)=2*b(n-1)</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(n)=b(n-1)</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(n)=2*b(n)</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);"><br></span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(1)=b(2)=2^1</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(3)=b(4)=2^2</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);"><br></span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(100)=2^50, &nbsp;b(100)=b(99)</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(97)=2^49, b(98)=b(97)</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);">b(96)=2^48, b(96)=b(95)</span></font></div><div><font color="#222222" face="Arial, Helvetica, sans-serif"><span style="font-size: 15px; line-height: 22px; background-color: rgb(255, 255, 255);"><br></span></font></div>
on 25-Aug-2014 17:42

<span style="font-weight: bold;">how to find that b(100)-b(97)-b(96)=2^50-2^49-2^48???</span>
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)
on 24-Sep-2016 10:25

Ans: 2^48<br>b(1) = 2*b(1-1) = 2*1 =&nbsp; 2<br>b(2) = b(1) = 2<br>b(3) = 2*b(2) = 2*2 = 4<br>b(4) = b(3) = 4<br>b(5) = 2*4 = 8<br>b(6) = 8<br>Hence b(100)-b(97)-b(96) = 2^50 - 2^49 - 2^48<br>= 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