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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;
What is Converse, Inverse, and Contrapositive In geometry, many declarations are written in conditional form "If ...., then....." For Example: "If two angles are right angles,
prove that every non-trivial ingetral solution (x,y,z)of the diophantine equation Xsquare +Ysquare=Zsquare satisfies gcd(x,y)=gcd(x,z)=gcd(y,z)
Last year Jonathan was 603/4 inches tall. This year he is 651/4 inches tall. How many inches did he grow? Subtract to find outthe difference in heights. You will need to borro
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Classify the following discrete-time signals as energy or power signals. If the signal is of energy type, find its energy. Otherwise, find the average power of the signal. X 1
Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon
real numbers?
Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)
Data entry is performed in 2-person teams. Each 2-person team can enter 520 surveys per day. A selection of 7540 surveys must be entered by day''s end. How many total employees, wo
two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent
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