6 votes 6 votes Consider a sequence of non-negative numbers ${x_{n} : n = 1, 2, . . .}$. Which of the following statements cannot be true? $\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$. $\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}< \infty$. $\sum ^{\infty }_{n=1} x_{n}< \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}< \infty$. $\sum ^{\infty }_{n=1} x_{n}\leq 5$ and $\sum ^{\infty }_{n=1} x_{n}^{2}\geq 25$. $\sum ^{\infty }_{n=1} x_{n} < \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$. Quantitative Aptitude tifr2014 quantitative-aptitude number-series + – makhdoom ghaya asked Nov 9, 2015 • edited Aug 15, 2020 by soujanyareddy13 makhdoom ghaya 989 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Rupendra Choudhary commented Dec 3, 2017 reply Follow Share This is an enthralling question certainly. Great Ramanujan proved the sum of infinite natural numbers to be -1/12 sources : https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF https://www.quora.com/Whats-the-intuition-behind-the-equation-1+2+3+-cdots-tfrac-1-12?redirected_qid=1559081 infinity is an lucrative number. Many scientists spent even more than half of their life only in trying to know what this infinity is. There was one of such great Mathematician "Georg cantor". interesting documentary created by BBC https://www.youtube.com/results?search_query=dangerous+knowledge i don't know answer of this question , but those are details i wished to share. 2 votes 2 votes sid816 commented Aug 19, 2020 reply Follow Share According to TIFR website the correct answer is option (e) 1 votes 1 votes Please log in or register to add a comment.
1 votes 1 votes I think (b) could be the answer, because if summation of Xn=infinite,then summation of Xn^2 cannot be less than Xn value srestha answered Nov 10, 2015 srestha comment Share Follow See all 5 Comments See all 5 5 Comments reply Himanshu1 commented Nov 20, 2015 reply Follow Share Why not (e)? 0 votes 0 votes srestha commented Nov 20, 2015 i edited by srestha Nov 20, 2015 reply Follow Share see, what I thought for example Can (1+2+3)=6 then (12+22+32)<6? No.right? But (b) says it is possible Same if 1+2+......+n=infinity Can 12+22+...........n2<infinity? (e) could be a correct ans, but ques asking for cannot be true 0 votes 0 votes Himanshu1 commented Nov 20, 2015 reply Follow Share Ya , right, But same with (e).. How can (e) be True?? Can u give an instance for that too.. 0 votes 0 votes srestha commented Nov 21, 2015 reply Follow Share No, (e) is like (1+2+3)<14 then (12+22+32)=14 , right? put infinite some value and check See there may be other logic possible, but my logic is this 0 votes 0 votes Himanshu1 commented Nov 21, 2015 reply Follow Share If (1+2+3)<∞ then (12+22+32) should also be less than ∞. How can it be equal to ∞.. 1 votes 1 votes Please log in or register to add a comment.