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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;
Topic : Use of Electronic whiteboards (ICT) in primary education in Australia and international. What are the key theories, concepts and ideas related to your topic? Wha
5 2 ----- - ----- x-1 x+1 -------------------- x 1 ----- + ----- x-1 x+1
Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x) dx Solution This kind of integral approximately falls into the form given in 3c. It is a quotient of ta
please help me in my assignment, explain Applications of Markov Chains in Business.
Equation s(in Tth second)=u+at-a/2 seems to be dimensionally incorrect.why?
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Mathematical Statements Are Unambiguous : Consider any mathematical concept that you're familiar with, say, a sphere. The definition of a sphere is clear and precise. Given any o
Example Find the values of the given expressions. Also given that a = 2, b = 3, c = 1, and x = 2. 8a + 5bc = 8.2
(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph. (b) Let G be a non directed gra
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