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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 remainder when 7^103 is divided by 24 Solution) we know by the concept of mod that..... 49 is congruent to 1 mod 24(means if 1 is subtracted fom 49 u get 48 which is
HOW MUCH WILL A NEW CAR COST? THE AVERAGE COST OF A NEW CAR IN 1990 WAS $14371. IN 2003 THE AVERAGE COST HAD RISEN TO $22360. WHAT IS THE AMOUNT OF THE MONTHLY PAYMENT? THE AMOUNT
t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........ 1 + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema
larry spends 3/4 hours twice a day walking and playing with his dog. He spends 1/6 hours twice a day feeding his dog. how much time does larry spend on his dog each day?
#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c
how much it cost an hour
prove that - there is one and only one circle passing through three non - collinear points
The complete set of all solutions is called as the solution set for the equation or inequality. There is also some formal notation for solution sets. We have to still acknowledge
set theory
One of the more significant ideas that we'll be discussing in this section is slope. The slope of a line is a measure of the steepness of any particular line and it can also be uti
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