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lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x?Ans) all no.s are positive or 0. so limit is either positive or 0.........(1)now {x}<=1;{2x}<=1;......{x}+{2x}+....{nx}<=nthat implies lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity n/n^2;that means lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity 1/n i.e. 0........(2)from (1) and (2);required limit=0;
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Maths For Fun : Often, when I have time on my hands, I try to solve interesting mathematical questions of the following kind. Sometimes my friends and I create the problems, and
Working Definition of Limit 1. We state that if we can create an as close to L like we want for all adequately large n. Alternatively, the value of the a n 's approach
The first year of the Islamic calendar marks the following event: The birth of Muhammad The Qu'ran is assembled into a single sacred text The division of the Sunnis and the Shiites
What is Congruent Number?
some basics problems to work
if an object weighed 11 pounds how many ounces would it weigh
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a die was rooled 500 times and number of times 4 came up was noted if the imperical probability calculated from this information 7_10
give the solution
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