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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;
Find models of energy production and energy usage from 2 different countries, each on a different continent, which predict future energy production and demands. How was data collec
Minimum and Maximum Values : Several applications in this chapter will revolve around minimum & maximum values of a function. Whereas we can all visualize the minimum & maximum v
I have a simple right angle triangle. All I am given is h (the hypotenuse) and that ratio of x:y is 2:3. What is the formula to find x and y in terms of h?
what is the differeance in between determinate and matrix .
z+31=73 for z=42
nc6:n-3c3=91:4
Consider the subsequent IVP. y' = f(t,y) , y(t 0 ) = y 0 If f(t,y) and ∂f/∂y are continuous functions in several rectangle a o - h o + h which is included in a
Ok this is true or false wit a definition. The GCF of a pair of numbers can never be equal to one of the numbers.
what is share and dividend?
The area of a square is 64 cm 2 . What is the length of one side of the square? To find out the area of a square, you multiply the length of a side through itself, because all
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