Search for: f [x] denotes the greatest integer less than or equal to x ,then limn→∞ [x]+[2x]+[3x]+….+[nx]n2 equal f [x] denotes the greatest integer less than or equal to x ,then limn→∞ [x]+[2x]+[3x]+….+[nx]n2 equal Ax/2Bx/3CxD0 Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:For any integer k, we havekx−1<[kx]≤kx⇒∑k=1n (kx−1)<∑k=1n [kx]≤∑k=1n kx⇒1n2∑k=1n (kx−1)<1n2∑k=1n [kx]≤1n2∑k=1n kx⇒xn2∑k=1n k−1n2<1n2∑k=1n [kx]≤xn2∑k=1n k⇒x21+1n−1n2<1n2∑k=1n [kx]≤x21+1nNow, limn→∞ x21+1n−1n2=x2 and , limn→∞ x21+1n=x2=limn→∞ 1n2∑n [kx]=x2 [Using Sandwich Theorem]i .e.limn→∞ [x]+[2x]+[3x]+…+[nx]n2=x2 Related content Oppositional Defiant Disorders Good Friday Wishes CBSE Class 9 Physics Motion Worksheet Autism Spectrum Disorder Sine and Cosine Waves Hindu Festivals List 2024 JEE Main Eligibility Criteria 2024 Session 2 (Released), Age Limits, Qualifying Marks, and Important Factor MCQs on Plant Hormones Class 10 5 Reasons To Choose The Commerce Stream After 10th Fl Words