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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;
Describe differance between Mean vs. Mode ? Every set of numbers or data has a mean and a mode value. The mean is the average value of all the numbers in the set. The mode is t
What is Permutations explain with examples? Each arrangement of a set of elements is called a permutation. In other words, every possible way (order) of writing a group of lett
Justin earned scores of 85, 92, and 95 on his science tests. What does he required to earn on his further science test to have an average (arithmetic mean) of 93%? To earn an a
It takes the moon an average of 27.32167 days to circle the earth. Round this number to the closest thousandth. The thousandths place is the third digit to the right of the dec
A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9. What is the probability that the product xy of the two
Is usual topology on R is comparable to lower limit topology on R
Changing The Base Of The Index For comparison reasons if two series have different base years, this is difficult to compare them directly. In such cases, it is essential to ch
how can we write the project
provide a real-world example or scenario that can be express as a relation that is not a function
A retired couple has up to $30000 to invest in fixed-income securities. Their broker recommends investing in two bonds: one a AAA bond yielding 8%; the other a B+ bond paying 12%.
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