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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;
Maya gives the children examples of distributive with small numbers initially, and leads them towards discovering the law. The usual way she does this is to give the children probl
of all those survey 390 were under 18 years of age if 20%were 18, how many responded to the survey
Derivative for Parametric Equations dx/dy = (dx/dt) / (dy/dt) , given dy/dt ≠ 0 Why would we wish to do this? Well, remind that in the arc length section of the Appl
Determine the Measurements of Segments and Angles Postulate 1.5 (The Distance Postulate) There is a unique positive number corresponding to every pair of points. Pos
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Chi Square Distribution Chi square was first utilized by Karl Pearson in 1900. It is denoted by the Greek letter χ 2 . This contains only one parameter, called the number of d
Multiply following. (a) (4x 2 -x)(6-3x) (b) (2x+6) 2 Solution (a) (4x 2 - x )(6 - 3x ) Again we will only FOIL this one out. (4x 2 - x )(6 - 3x) = 24x 2 -
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