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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 the equation of the plane through (2, 1, 0) and parallel to x + 4y 3z = 1.
three towns are situated in such away that town B is 120 kilometers on a bearing of 030 degrees from town A. Town C is 210 kilometers on a bearing of 110 degrees from town A (a)ca
Determine how many different words can be formed out of the letters of the word VARANASI? Ans: 720 different words can be formed out of the letters of the word VARANASI.
what is prime factorization of 200
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
A 125-foot tower is located on the side of a mountain that is inclined at 32° to the horizontal. A guy wire is to be fitted to the top of the tower and anchored at a point 55 feet
You know the experation for the area of a circle of radius R. It is Pi*R 2 . But what about the formula for the area of an ellipse of semi-minor axis of length A and semi-major
i need help with 3x+5y=7 2x-5y=8
Determine equation of the tangent line to f (x) = 4x - 8 √x at x = 16 . Solution : We already know that the equation of a tangent line is specified by,
give me the derivation of external division of sectional formula using vectors
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