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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;
Calculate the area of RECTANGLE ? The area of a rectangle is the amount of space taken up by a rectangle, which is a two-dimensional shape. You find the area (A) of a recta
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
Anne, Betty and Carol went to their local produce store to buy some fruit. Anne bought one pound of apples and two pounds of bananas and paid $2.11. Betty bought two pounds of appl
Calculate subsequent proportion: A recipe calls for 1(1/2) cups of flour to make servings for 6 people. How much flour should be used to make servings for 4 people? Solut
The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions
New England University maintains a data warehouse that stores information about students, courses, and instructors. Members of the university's Board of Trustees are very much inte
The angles between three non-zero and non coplanar vectors a,b and c are α between b and c and β between c and a and γ between a and b. The vector u and v are defined by u=(aX
Ribbon is wrapped around a rectangular box that is 10 by 8 by 4 in. Using the example provided, calculate how much ribbon is needed to wrap the box. consider the amount of ribbon d
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
You have just renegotiated the interest rate of your home mortgage loan. (This is called rate modification.) The original loan of $400,000 carries an interest rate is 6% has an or
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