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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;
On your geometry test you have two triangles: ?ABC and ?MNO. You are told that ?A ? ? M and that ?B ? ? N. Which statement is also true?
1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o
Determine how many square centimeters of paper are needed to make a label on a cylindrical can 45 cm tall with a circular base having diameter of 20 cm. Leave answer in terms of π.
without a calculator give the exact value of each of the following logarithms. (a) (b) log1000 (c) log 16 16 (d) log 23 1 (e) Solution (b) log10
Determine or find out if the subsequent series is convergent or divergent. If it converges find out its value. Solution To find out if the series is convergent we fir
In Figure, what are the angles of depression from the observing positions O 1 and O 2 of the object at A?
In algebra knowing that 2 3 = 8 is not sufficient. Equally important to know is what would be the result if quantities like 2 3 . 2 -4 . 2 6 or 3 7 / 3 2
The sum of areas of two squares is 468m 2 If the difference of their perimeters is 24cm, find the sides of the two squares. Ans: Let the side of the larger square be x .
round to the nearest hundreths 1677.76
Rick is order a latest triangular sail for his boat. He needs knowing the area of the sail. Which formula will he use? The area of a triangle is 1/2 times the length of the bas
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