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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;
Proof of Limit Comparison Test As 0 Now, as we know that for large enough n the quotient a n /b n should be close to c and thus there must be a positive integer
Explain How to Distribute simplifying expressions? The distributive law states that for all numbers a, b, and c, a(b + c)= ab + ac What does this mean in plain language?
Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi
A particle moves along a straight line so that after t secs its distance from fixed point O on the line is given by s=(t-1)^2(t-2).find the distance from O when the velocity is zer
I am looking for a tutor in College Algebra
If I divide any number do I get the manservant 2 times
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4into 5 is;
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