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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;
1. Find the slope and the y-intercept of the line whose equation is 5x + 6y = 7. 2. Find the equation of the line that is parallel to 2x + 5y = 7 and passes through the mid poin
The last topic that we want to discuss in this section is that of intercepts. Notice that the graph in the above instance crosses the x-axis in two places & the y-axis in one plac
algorithm and numerical examples of least cost method
what is the business application of matrices
Grimm plc (Grimm) has the following transactions: a) On 1 st January 2010, Grimm issued 400,000 convertible £1 6% debentures for £600,000. The professional fees associated wit
Q. What is the probability of tossing a head? List the sample space for tossing a coin once. What is the probability of tossing a head? Solution: If you tossed a coin once
13+13
why
The area of a rectangle gets decreased by 8 m2, if its length is decreased by 5 m and breadth increased by 3 m. If we enhance the length by 3 m and breadth by 2 m, the area is en
Recognizes the absolute extrema & relative extrema for the given function. f ( x ) = x 2 on [-2, 2] Solution Following is the graph for this fun
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