Ratio

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Fri Feb 19, 2010 12:36 pm
Location: Pennsylvania
Thanked: 1 times

Ratio

by tsmith93 » Mon Mar 15, 2010 1:56 am
For any positive integer a: <<a>> = 1/2^(a+1)

What is the ratio of <<a+3>> to <<a>>?
Source: — Problem Solving |

User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Mon Mar 15, 2010 2:16 am
tsmith93 wrote:For any positive integer a: <<a>> = 1/2^(a+1)

What is the ratio of <<a+3>> to <<a>>?


<<a+3>> = 1/2^(a+3+1) = 1/2^(a+4) = 1/2^3 * 1/2^(a+1) = 1/2^3*<<a>>

=> <<a+3>>/<<a>> = 1/2^3 = 1/8
Always borrow money from a pessimist, he doesn't expect to be paid back.