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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;
There are k baskets and n balls. The balls are put into the baskets randomly. If k
how do i know what operation to use in a fraction word problem
y 2 = t 2 - 3 is the actual implicit solution to y'= t/y, y(2) = -1. At such point I will ask that you trust me that it is actually a solution to the differential equation. You w
similar triangles diagram
Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r
A passenger jet took 3 hours to fly 1800 km in the direction of the jetstream. The return trip against the jetstream took four hours. What was the jet's speed in still air and the
If sin? = 1/2 , show that 3cos?-4cos 3 ? = 0. Ans: Sin ? = ½ ⇒ ? = 30 o Substituting in place of ? =30 o . We get 0.
Graph ( x - 2) 2 /9+4(y + 2) 2 = 1 Solution It is an ellipse. The standard form of the ellipse is ( x - h
To help Himalya herbal launch a successful marketing campaign in the UK
We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now. Sin
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