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 1.1k 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.