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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;
Explain the Vertex Formula ? The vertex formula is a convenient way of finding the vertex of the graph for any quadratic function. The graph of the quadratic equation f(x) = ax
a statisics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. find the probability that a given class pe
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Find all the eighth roots of (19 + 7 i)
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Definition 1. Given any x 1 & x 2 from an interval I with x 1 2 if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2. Given any x 1 & x 2 from an interval
Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon
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