0 votes 0 votes What’s the trick to do it under 2 min here? Combinatory made-easy-test-series recurrence-relation + – shaz asked Dec 31, 2018 • edited Mar 4, 2019 by Rishi yadav shaz 1.2k views answer comment Share Follow See all 22 Comments See all 22 22 Comments reply bhanu kumar 1 commented Dec 31, 2018 reply Follow Share Is answer :[ 17+ log(17)] ? 0 votes 0 votes akshat sharma commented Dec 31, 2018 reply Follow Share a(n)=n*2^n will be recurrence relation answer is 21 0 votes 0 votes bhanu kumar 1 commented Dec 31, 2018 reply Follow Share How have you solved this please Explain? 0 votes 0 votes shaz commented Dec 31, 2018 reply Follow Share @akshat please explain how you arrived at this answer. 0 votes 0 votes shaz commented Dec 31, 2018 reply Follow Share @bhanu Answer is 21 so yes yours is very close. How did you go about it 0 votes 0 votes bhanu kumar 1 commented Dec 31, 2018 reply Follow Share @shaz ........ by solving Recurrence relation i get simplified for a(n)= n*2^n ; a17=17* 2^17=X ; and taking log of it. 0 votes 0 votes shaz commented Dec 31, 2018 reply Follow Share that is my question, how exactly is it being simplified? 0 votes 0 votes MiNiPanda commented Dec 31, 2018 reply Follow Share $a_n=4(a_{n-1} - a_{n-2})$ Let $a_n=r^n$ Then, $r^n=4(r^{n-1} - r^{n-2})$ => $r^2=4(r-1)$ =>$r^2- 4r +4 =0$ =>$(r-2)^2=0$ r=2,2 $a_n= \alpha \times (2)^n + \beta \times n \times (2)^n$ ....[solving linear homogenous recurrence relation] $n=1, a_n=2$ $2= 2\alpha + 2\beta$ $1= \alpha + \beta$ --> (1) $n=2, a_n=8$ $8= \alpha \times 4 + \beta \times 2\times 4$ =>$2= \alpha + 2\beta$ --> (2) From (1) and (2) $\alpha= 0,\beta=1$ So, $a_n=n2^n$ [But they have got $\alpha= 1, \beta=-1$ I don't know how $|X|=a_{17}=17*2^{17}$ $log_2|17*2^{17}|= log_2|17|+17log_2(2)=4.08+17=21.08 \approx 21$ I agree with @bhanu kumar 1 @akshat sharma Are you getting exact 21? 4 votes 4 votes akshat sharma commented Dec 31, 2018 reply Follow Share no i have taken absolute value @MiNiPanda correct approach ,) 0 votes 0 votes Navneet Kalra commented Jan 4, 2019 reply Follow Share absolute value is on X not on whole part.....so answer should be 21.08...not 21 0 votes 0 votes Ramij commented Jan 8, 2019 reply Follow Share can anyone explain the answer i didnt get it 0 votes 0 votes Gate Fever commented Jan 12, 2019 reply Follow Share an=α×$(2)^n$+β×n×$(2)^n$ ....[solving linear homogenous recurrence relation] why u took this eqn?? @MiNiPanda whats wrong with this,we always take this eqn only!!(given below) $a_{n}$=u*$(2)^{n}$ + v * $(2)^{n}$ 0 votes 0 votes Gate Fever commented Jan 12, 2019 reply Follow Share @shaz when u ask question next time, make sure u write it and dont post the screen shots because it is very difficult to find a question that is already asked and has got a best solution too. if u type it, it is easier for others also to see that doubt and there are less no. of duplicate question too. Its a humble request, please follow this from next time!! 0 votes 0 votes MiNiPanda commented Jan 12, 2019 reply Follow Share @Gate Fever For distinct roots we take the equation given by you.. but here we are getting equal roots. So use the other equation.. 1 votes 1 votes Gate Fever commented Jan 12, 2019 reply Follow Share @MiNiPanda is there any other case also? 0 votes 0 votes MiNiPanda commented Jan 12, 2019 reply Follow Share For linear homogenous rec relation, these 2 are the only cases.. 1 votes 1 votes Gate Fever commented Jan 12, 2019 reply Follow Share ok 0 votes 0 votes shaz commented Jan 15, 2019 i edited by shaz Jan 15, 2019 reply Follow Share For those not familiar with Linear homogeneous recurrence relation like me watch this video for understanding. 0 votes 0 votes shaz commented Jan 16, 2019 reply Follow Share @MiNiPanda Actually there's also a third case where we get complex roots. 1 votes 1 votes MiNiPanda commented Jan 16, 2019 reply Follow Share @shaz Oh yes you are right..forgot about it..can you please write it down here? 0 votes 0 votes Gate Fever commented Jan 16, 2019 reply Follow Share yes pls write it here @shaz 0 votes 0 votes shaz commented Jan 16, 2019 reply Follow Share watch this video for complex root type : https://youtu.be/0kkY9D6baRY 0 votes 0 votes Please log in or register to add a comment.