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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;
write and solve a problem of multiplacation that uses: estimate explaning numbers picturs and another operation?
These experiences should be related to the mathematical concepts and ideas that we teach them. Only then will these ideas appear relevant to the children, and be absorbed by them
which quadrilaterals have only 1 pair of parallel sides
In figure, the incircle of triangle ABC touches the sides BC, CA, and AB at D, E, and F respectively. Show that AF+BD+CE=AE+BF+CD= 1/2 (perimeter of triangle ABC), Ans:
Find The Ratio Of : 2 dozens to a score
what''s it?
There isn't actually a whole lot to this section this is mainly here thus we can get several basic concepts and definitions out of the way. Most of the concepts and definitions in
Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves. Note also that we said "enclosed by" in place of "under" as we usually have
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
conclusion for the shares nd dividends
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