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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;
The sum of -4 and a number is equal to -48. What is the number? Let x = the number. Because sum is a key word for addition, the equation is -4 + x = -48. Add 4 to both sides o
Harold used a 3% iodine solution and a 20% iodine solution to make a 95- ounce solution in which was 19% iodine. How many ounces of the 3% iodine solution did he use? Let x = t
Lines- Common Polar Coordinate Graphs A few lines have quite simple equations in polar coordinates. 1. θ = β We are able to see that this is a line by converting to Car
INTRODUCING COUNTING : From what you studied previous study, you know what it means to count. You would also agree that rote learning of number names does not always mean that the
give an example of a binomial of degree 27?
what is the answer to 2.1 to 4.2
Stratified sampling In stratified sampling case the population is divided into groups in such a way that units in each group are as same as possible in a process called strati
design a synchronous, recycling, MOD-12 counter with D FF''s. Use the states 0000 through 1011 in the counter.
Properties of Integration
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
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