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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;
compare: 643,251: 633,512: 633,893. The answer is 633,512.
project assignment of page no.19 question no.2
give an example of a binomial of degree 27?
Ryan's gym membership costs him $390 per year. He pays this within twelve equal installments a year. How much is every installment? To ?nd out each installment, the total yearl
-9/5 / 2
Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha
Consider the following set of preference lists: Number of Voters (7) Rank 1 1
find the composition of the simple harmonic motion of the same period in the perpendicular directions
what is the greatest projection range down an inclined plane? how we will calculate that?
Two angles are complementary. The calculate of one angle is four times the measure of the other. Evaluate the measure of the larger angle. a. 36° b. 72° c. 144° d. 18°
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