If-n-Z-prove-that-1-2-1-1-3-2-1-4-3-1-n-1-n-lt-2- Tinku Tara June 4, 2023 None 0 Comments FacebookTweetPin Question Number 113070 by ZiYangLee last updated on 11/Sep/20 Ifn∈Z+,provethat121+132+143+…1(n+1)n<2 Answered by 1549442205PVT last updated on 11/Sep/20 Wehave1(n+1)n=n.1(n+1)n=n(1n−1n+1)=n(1n+1n+1)(1n−1n+1)=(1+1n+1)(1n−1n+1)Since(1+1n+1)<2,so[1(n+1)n]<2(1n−1n+1).Hence,given=1,2,…weget121=12<2(11−12),132<2(12−13),…,1(n+1)n<2(1n−1n+1)AddingupnaboveinequalitieswegetLHS=121+132+143+…1(n+1)n<2[11−12+12−13+…+1n−1n+1)=2(1−1n+1)<2Therefore,wehave121+132+143+…1(n+1)n<2(q.e.d) Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: 400-2-100-2-Next Next post: Question-178609 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.