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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;
The sum of -4 and a number is equal to -48. What is the number? Let x = the number. Because sum is a key word for addition, the equation is -4 + x = -48. Add 4 to both sides o
Maxima and Minima We have to make a distinction between relative maxima (or minima) and global maxima (or minima). Let f(x) be a function of x. Then the global maxi
As a creative and innovative entrepreneur, we are required to invent or improvise a product or service that benefits the society and the economy, so what do you think is it?
(1) The following table gives the joint probability distribution p (X, Y) of random variables X and Y. Determine the following: (a) Do the entries of the table satisfy
Raul has 56 bouncy balls. He puts three times as many balls into red gift bags as he puts into green gift bags. If he puts the same number of balls in each bag, how many balls does
Joe took out a car loan for $12,000. He paid $4,800 in interest at a rate of 8% per year. How many years will it take him to pay off the loan? Using the easy interest formula I
Assume that (X, d) is a metric space and let (x1, : : : , x n ) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , x n ) obtain
If you find nothing out of this rapid review of linear algebra you should get this section. Without this section you will not be capable to do any of the differential equations wo
find the sum of the following series upto n terms: 1*2+2*4+3*8+4*16+.....
Catalans Conjecture
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