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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;
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The Hurwiz method Hurwiz method was the concept of coefficient of optimism or pessimism introduced by L. Hurwicz. The decision maker takes into account both the minimum and max
i want to find the solution for exercises
Prove that the Digraph of a partial order has no cycle of length greater than 1. Assume that there exists a cycle of length n ≥ 2 in the digraph of a partial order ≤ on a set A
Repetition Need Not Be Boring : From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an
Q. What are Inclusive Events? Ans. Events that can occur at the same time are called inclusive events. For example, a student can belong to more than one club at one time
If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c please explain. Solution) (x-p)(x-q)=c x2-(p+q)x-c=0 hence, a+b=p+q and a.b=pq-c
27-125 a power -135a +225a power2
A Cleaning solution has 40% vinegar. Find the amount of vinegar in 32 ounces of the solution>
change 5.075 to a fraction
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