bobsmegdorf Posted September 23, 2013 Report Share Posted September 23, 2013 (edited) Recursive formula Edited October 7, 2013 by bobsmegdorf Reply Link to post Share on other sites More sharing options...
ctrls Posted September 23, 2013 Report Share Posted September 23, 2013 I'm guessing you have to prove the general solution to be and for all positive integers?Proving it for n=1 is simple since it's given it's a base case, then you just assume . Since the next case n+1 can be expressed using the recurrence relation as , you just have to substitute Tn with the general solution you assumed. With a bit of rearranging you will end up at , which is the required result. 1 Reply Link to post Share on other sites More sharing options...
-._._.- Posted September 23, 2013 Report Share Posted September 23, 2013 Love mathematical induction.The beauty of the concept. 2 Reply Link to post Share on other sites More sharing options...
rinik Posted September 23, 2013 Report Share Posted September 23, 2013 (edited) Start by examining the relationFind a new way to write down the general termT(2) = 2*T(1) + 1T(3) = 2*T(2) + 1 T(4) = 2*T(3) + 1T(5) = 2*T(4) + 1now substitute the previous term in to the next T(3) = 2(2*T(1) + 1) +1 = 4*T(1) + 4 - 1 .............There is a reason I am writing 3 as 4 - 1 just follow the stuff belowT(4)= 8*T(1) + 8 -1analyze the above and deduce thatT(n) = 2^(n-1)*T(1) + 2^(n-1) - 1Prove by mathematical inductionshow for n =some numberassume n=kT(k) = 2^(k-1)*T(1) + 2^(k-1) - 1Prove for T(k+1)T(k+1) = 2 * (2^(k-1) T(1) + 2^(k-1) - 1) + 1just simplify this and you will get what you are looking for then substituent it with 2 * T(k) + 1 I took some time and did some research and I think this will answer all the questions you have http://www.math.dartmouth.edu/archive/m19w03/public_html/Section4-2.pdfYou will also see that there are other ways to approach this.You won't see problems like these in final IB exams. If you are not doing this for your EE or portfolio stop and practice for the final exams this will just distract you from the things you need to know. Coming from a person who loves mathematics and is trying to get accepted to a good uni at the moment Edited September 25, 2013 by rinik 2 Reply Link to post Share on other sites More sharing options...
bobsmegdorf Posted September 29, 2013 Author Report Share Posted September 29, 2013 (edited) thanks Edited October 7, 2013 by bobsmegdorf Reply Link to post Share on other sites More sharing options...
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