Math Goodies is a free math help portal for students, teachers, and parents.
|
Interactive Math Goodies Software

Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
 All Forums  Homework Help Forums  Miscellaneous Math Topics  Need Help with this Discrete Math problem New Topic  Topic Locked  Printer Friendly
Author  Topic

clavezza
New Member

USA
2 Posts

 Posted - 08/31/2007 :  23:17:01 I am not sure how to solve this particular problem:2 + 6 + 18 + ... + 2 * 3 to the n-1 power = 3n - 1Thanks for the helpChris

Ultraglide

278 Posts

 Posted - 09/01/2007 :  00:42:41 I'm not sure what your problem is, could you clarify it?

Ultraglide

278 Posts

 Posted - 09/01/2007 :  00:43:54 Is it a summation? Are you proving by induction?

Subhotosh Khan

USA
9114 Posts

 Posted - 09/01/2007 :  12:23:35 quote:Originally posted by clavezzaI am not sure how to solve this particular problem:2 + 6 + 18 + ... + 2 * 3 to the n-1 power = 3n - 1Thanks for the helpChrisFactor out 2 - then you have a GP series.

clavezza
New Member

USA
2 Posts

 Posted - 09/01/2007 :  12:35:00 SOrry,Suppose to use mathematical induction to prove that the statements are true for every positive integer n.chris

sahsjing

USA
2399 Posts

 Posted - 09/01/2007 :  19:51:07 n = 12 = 3^(1)-1 It works.Assume at n = k, 2 + 6 + 18 + ... + 2 * 3 ^(k-1) = 3^(k) - 1At n = k+1,2 + 6 + 18 + ... + 2 * 3 ^k= 2 + 6 + 18 + ... + 2 * 3 ^(k-1) + 2*3^k= 3^(k) - 1 + 2*3^k= 3^k(1+2)-1= 3^(k+1) - 1
Topic
 New Topic  Topic Locked  Printer Friendly Jump To: Select Forum New Visitor Forum       Testing Forum Homework Help Forums       Basic Math and Pre-Algebra       Algebra       Geometry and Trigonometry       Pre-Calculus and Calculus       Probability and Statistics       Standardized Test Preparation Help       Miscellaneous Math Topics Educator Forum       Teacher Talk Parent Forum       Parent's Place  -------------------- Home Active Topics Frequently Asked Questions Member Information Search Page
 Math Forums @ Math Goodies © 2000-2004 Snitz Communications