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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;
Finding derivatives
From a fixed point directly in front of the center of a bull's eye, Kim aims two arrows at the bull's eye. The first arrow nicks one point on the edge of the bull's eye; the second
I just have a hard time in math in every other class I have an A or B but in math I have a C+ I at least want a B- or B+ or A- or even an A+
jack and his mother paid $11.50 for tickets to the movies. An adult''s ticket costs $4.50 more than a child''s ticket. What was the cost of each ticket?
Longer- Term Forecasting Moving averages, exponential smoothing and decomposition methods tend to be utilized for short to medium term forecasting. Longer term forecasting is
Write the next two terms √12, √27, √48, √75................... Ans: next two terms √108 , √147 AP is 2 √3 , 3 √3 , 4 √3 , 5 √3 , 6 √3 , 7 √3 ......
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Advantages and disadvantages of operation researchs
a company declares a semu annual dividend on 5%.a man has 400 shares of the company.if his annual income from the share is rs 1000 find the face value of each share?
Area Problem Now It is time to start second kind of integral: Definite Integrals. The area problem is to definite integrals what tangent & rate of change problems are to d
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