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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;
Comparison - the difference between two groups or numbers, namely, how much one is greater than the other, how much more is in one group than in the other. (e.g., if Munna has
In multiplication and division we have 1) Suggested ways of conveying the meaning of multiplication and division to children. These operations have to be taught as an activit
A farmer's rectangular field has an area in which can be expressed as the trinomial x2 + 2x + 1. In terms of x, what are the dimensions of the field? Because the formula for th
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
1) At a midway game at the state fair, the probability of winning an individual game is advertised to be 30% ( p = . 3). Suppose 50 people played the game (assume all 50 outcomes
Expected Value of Perfect Information In the above problems we have used the expected value criterion to evaluate the decisions under the conditions of risk. But, as long as un
solutions for the equation a-b=5
Definition 1. Given any x 1 & x 2 from an interval I with x 1 2 if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2. Given any x 1 & x 2 from an interval
Derivative with Polar Coordinates dy/dx = (dr/dθ (sin θ) + r cos θ) / (dr/dθ (cosθ) - r sinθ) Note: Rather than trying to keep in mind this formula it would possibly be easi
If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0
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