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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;
let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?
Logarithm Functions : Now let's briefly get the derivatives for logarithms. In this case we will have to start with the following fact regarding functions that are inverses of ea
A school principal is looking at the combinations of subjects students are studying. He learns that the probability that a student is studying Chemistry is 0.5 and that the prob
how to do them?
ABC is a right-angled isosceles triangle, right-angled at B. AP, the bisector of ∠BAC, intersects BC at P. Prove that AC 2 = AP 2 + 2(1+√2)BP 2 Ans: AC = √2AB (Sinc
Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?
How can i calculate arc length for dividing a circle into 10 parts
Find out the center of mass for the region bounded by y = 2sin (2x), y =0 on the interval [0 , Π/2] Solution Here is a sketch (diagram) of the region along with the cent
Determining the Laplace transform of a function is not terribly hard if we've found a table of transforms opposite us to use as we saw in the previous section. What we would want t
There is a committee to be selected comprising of 5 people from a group of 5 men and 6 women. Whether the selection is randomly done then determines the possibility of having the g
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