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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;
Proof of Alternating Series Test With no loss of generality we can assume that the series begins at n =1. If not we could change the proof below to meet the new starting place
tanx dx
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Solving Trig Equations with Calculators, Part I : The single problem along with the equations we solved out in there is that they pretty much all had solutions which came from a
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Negative function : Several functions are not positive however. Consider the case of f (x ) =x 2 - 4 on [0,2]. If we utilizes n = 8 and the midpoints for the rectangle height w
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can you help me with financial math??
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