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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;
Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.
Equal groupings - when we want to find how many objects there are in several equal-sized sets. (e.g., if there are 3 baskets, each with 4 bananas, 4 oranges and 4 apples, respec
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A well-known simple model, applicable for analysing boom-bust cycles in agriculture, but extendable to analysing boom-bust cycles in many different areas of economics is the hog cy
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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
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