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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;
limit x APProaches infinity (1+1/x)x=e
The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.
Frederick bought six books which cost d dollars each. What is the total cost of the books? Frederick would multiply the number of books, 6, through how much each one costs, d.
there are 5 small cubes and it reads the 5 small cubes is 1/100, then what is the ONE?
Review: Systems of Equations - The traditional initial point for a linear algebra class. We will utilize linear algebra techniques to solve a system of equations. Review: Matr
cos inverse x -cos inverse 2x=pie\2
Find all the eighth roots of (19 + 7 i)
Parametric objective-function problems
sin3θ = cos2θ find the most general values of θ satisfying the equatios? sinax + cosbx = 0 solve ? Solution) sin (3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos(
Q. Multiplying Fractions Involving Negative Numbers? Ans. If you have only one negative sign, the result is still negative: If you have more than one, just remembe
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