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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;
a mixture of 40 liters of milk and water contains 10% water.how much water should be added to this so that water my be 20% in the new mixture
ABC is a right angled triangle in which ∠A = 900. Find the area of the shaded region if AB = 6 cm, BC=10cm & I is the centre of the Incircle of ?ABC. Ans: ∠A =90 0 BC
On your geometry test you have two triangles: ?ABC and ?MNO. You are told that ?A ? ? M and that ?B ? ? N. Which statement is also true?
two consecutive integers sum to 39, what they?
Which of the partially ordered sets in figures (i), (ii) and (iii) are lattices? Justify your answer. Ans: suppose (L, ≤) be a poset. If each subset {x, y} consisting
A firm buys a product using the price schedule given in the table: The company estimate holding costs at 10% of the purchase price per year and ordering costs at $40 per order .
Linear Approximation Method This is a rough and ready method of interpolation and is best used when the series moves in predicted interval
How do you multiply frations?
There's a nice way to show why the expresion for the area of a circle of radius R is: Pi * R 2 . It has an comman relationship with the experation for the circumference of a
Determine if the following sequences converge or diverge. If the sequence converges find out its limit. a. {3n 2 - 1 / 10n + 5n 2 } ∞ n =2 b. {e 2n / n} ∞ n =1 c
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