Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • if a and b are +ve integers then find [a/b]+[2a/b]+[3a/b]......[(b-1)a/b] where [.] denotes greatest integer function

if a and b are +ve integers then find [a/b]+[2a/b]+[3a/b]......[(b-1)a/b] where [.] denotes greatest integer function

Answers (1)

best_answer

we know    \frac{a}{b}<=\left [ \frac{a}{b} \right ]<\frac{a}{b}+1    (1)

let  U= [a/b]+[2a/b]+[3a/b]......[(b-1)a/b] 

and applying the (1) in every term we get

\left ( 1+2+...+b-1 \right )\frac{a}{b}<=U<\left ( 1+2+...+b-1 \right )\frac{a}{b}+\left ( b-1 \right )\times 1

=\frac{\left ( b \right )\left ( b-1 \right )}{2}\times \frac{a}{b}<= U < \frac{\left ( b \right )\left ( b-1 \right )}{2}\times \frac{a}{b} + \left ( b-1 \right )

=\frac{a\left ( b-1 \right )}{2}<=U<\frac{\left ( b-1 \right )\left ( a+2 \right )}{2}

Posted by

Randheer Kumar Gautam

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 applications close on November 27; apply at jeemain.nta.nic.in
anam-khan

JEE 2026: IIT admissions show major shift toward AI, data science, away from core engineering courses
anam-khan

JEE Main 2026: NIT Delhi cut-offs for BTech courses show ever-increasing demands for AI, computer skills

Latest Question