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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;
Difference between absolute and relative in the definition Now, let's talk a little bit regarding the subtle difference among the absolute & relative in the definition above.
2/2
Dividing a quantity in a given ratio
An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss
In a recent survey of 700 people, 15% said that red was their favorite color. How many people said that red was their favorite color? Find out 15% of 700 through multiplying 70
In a garden, 1/8 of the flowers are tulips. 1/4 of the tulips are red. What fraction of the flowers in the garden are red tulips?
Root Test- Sequences and Series This is the final test for series convergence that we're going to be searching for at. Like with the Ratio Test this test will as well tell wh
You are given the following regression results estimating the demand for widgets based on time series data for the past 40 months. Q t = 2.5 - 0.3 x P t + 12 x M t Where Q
Vector Form of the Equation of a Line We have, → r = → r 0 + t → v = (x 0 ,y 0 ,z 0 ) + t (a, b, c) This is known as the vector form of the equation of a line. The lo
application
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