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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;
Initial Conditions and Boundary Conditions In many problems on integration, an initial condition (y = y 0 when x = 0) or a boundary condition (y = y
If the distances from origin of the centres of 3 circles x 2 +y 2 +2alphaix= a 2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+
Proof of Root Test Firstly note that we can suppose without loss of generality that the series will initiate at n = 1 as we've done for all our series test proofs. As well n
In a digital filter, one of the parameters in its difference equation is given by the formula a) Show that the above formula has one horizontal and one vertical asymptote.
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The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers. Another definition of real numbers us
Sketch several trajectories for the system, x 1 ' = x 1 + 2x 2 x 2 ' = 3x 1 + 2x 2
Does neuro marketing give impetus to new consumer behaviour
As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic
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