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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;
If the areas of the circular bases of a frustum of a cone are 4cm 2 and 9cm 2 respectively and the height of the frustum is 12cm. What is the volume of the frustum. (Ans:44cm 2 )
Determine the centralizer and the order of the conjugacy: 1) Determine the centralizer and the order of the conjugacy class of the matrix [1, 1; 0, 1] in Gl 2 (F 3 ).
let X be a nonempty set. let x belong to X. show that the collection l={ union subset of X : union = empty or belong U
robin runs 5 kilometers around the campus in the same length of time as he can walk 3 kilometers from his house to school. If he runs 4 kilometers per hour faster than he walks, ho
maximize Z=2x+5y+7z, subject to constraints : 3x+2y+4z =0
Mary has $2 in her pocket. She does yard work for four various neighbors and earns $3 per yard. She then spends $2 on a soda. How much money does she have left? This translates
What is Geometry?
how do i round off $5.00 to the nearest 10
Using the example provided, Evaluate the area of the shaded region in terms of π. a. 264 - 18π b. 264 - 36π c. 264 - 12π d. 18π- 264 b. The area of the shaded r
Marci filled her car's gas tank on Monday, and the odometer read 32,461.3 miles. On Friday while the car's odometer read 32,659.7 miles and she filled the car's tank again. It will
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