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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;
Explain Comparing Mixed Numbers in maths? A mixed number is made up of two parts: a whole number and a fraction. For example: 2(3/4) 2(3/4) is read "two and three-fourths
Next we have to talk about evaluating functions. Evaluating a function is in fact nothing more than asking what its value is for particular values of x. Another way of looking at
(x+y+1)dy/dx=1
When Ms. Jones retired, she received a lump sum of $1,000,000 from her pension plan. She then invested this sum in an annuity account that would pay her an equal amount at the end
E1) Try and see the order in which different children fills numbers in the grid above. My claim is that all of them would fill in the ones, the fives and the tens first. Test my hy
Finding the Slope of a Line, Given Two Points on it ? Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4). One way to find the slope is
Example: Find out the radius of convergence for the following power series. Solution : Therefore, in this case we have, a n = ((-3) n )/(n7 n+1 ) a n+1 = (
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
sin (cot -1 {cos (tan -1 x)}) tan -1 x = A => tan A =x sec A = √(1+x 2 ) ==> cos A = 1/√(1+x 2 ) so A = cos -1 (1/√(1+x 2 )) sin (cot -1 {cos (tan -1 x)}) = s
would like explaination on how to do them
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