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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;
find the coordinates of points of tri-section of the line joining the points (-3,0) and (6,6).
A particular algebra text has a total of 1382 pages which is broken up into two parts. the second part of book has 64 more pages than first part. How many pages are in each part of
If F ( x,y, z) = x y² y4 i + ( 2x2 y + z) j - y3 z² k, find: i). question #Minimum 100 words accepted#
Deflation Indexes may be utilized to deflate time series so that comparisons among periods may be made in real terms. This is a process of decreases a value measured in cur
What is Dividing Fractions? If you want to divide two fractions, you invert the second fraction (that is, turn it upside-down) and change the division sign to a multiplication
State DeMorgan's law. Prove it using the truth table. Ans: DeMorgan's law defines that (i) (x ∨ y)' = x' ∧ y' (ii) (x ∧ y)' = x' ∨ y' Now let us dr
how do you find the length of a parallel line connecting two external circles of different sizes from the outside, given the value of both radius and one parallel line.
Standard Basis Vectors Revisited In the preceding section we introduced the idea of standard basis vectors with no really discussing why they were significant. We can now do
dividing decimals
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