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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;
what is meant by "measure of location"
a lending library has a fixed charge for the first three days and an additional charge for each day thereafter. sam paid Rs 27 for a bookkept for 7 days while jaan paid Rs 21 for t
what is sin, cos, and tan?
for what value of k,the following system of equations have infinite solutions?kx + 5y -(k-5)=0;20x +ky - k=0
Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du, where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably
A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just im
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f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .
Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied
(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co
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