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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;
Application of rate change Brief set of examples concentrating on the rate of change application of derivatives is given in this section. Example Find out all the point
Rule 1 The logarithm of 1 to any base is 0. Proof We know that any number raised to zero equals 1. That is, a 0 = 1, where "a" takes any value. Therefore, the loga
Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?
Complex Numbers In the radicals section we noted that we won't get a real number out of a square root of a negative number. For example √-9 isn't a real number as there is no
a) Let n = (abc) 7 . Prove that n ≡ a + b + c (mod 6). b) Use congruences to show that 4|3 2n - 1 for all integers n ≥ 0.
Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t
what is meant by "measure of location"
r=asin3x
9*9
Give me an example , please : 1 over 2 , 14 over twenty-eight
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