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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;
How did Rousseau resolve the conflict between the rights of the individual and the responsibilities of government (the state)? How did the ideas about universal education and socia
Evaluate the given definite integral. Solution Let's begin looking at the first way of dealing along with the evaluation step. We'll have to be c
Whlie solving complex number 1pi in polar form.In book they have taken theta =-pi/4 why not 7pi/4 because the point lie in fourth quadrant and the theta is given by 2pi-angle(alpha
How do I proceed with a project on Shares and Dividends?
find the radius of circumcircle of an equilateral triangle of 6root3 one side.
Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''''s encountered is even or odd.on..
For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia , f
2x-11x-21
PROOF OF VARIOUS DERIVATIVE FACTS/FORMULAS/PROPERTIES Under this section we are going to prove several of the different derivative facts, formulas or/and properties which we en
cramers rule introduction
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