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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;
Right-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x>a without in fact letting x be a.
together, pearl and harvey are going to visit their aunt on sunday. If Pearl visits their aunt every 6 days, while harvey every 8 days, on what day will they visit their aunt toget
Find out the determinant: Find out the determinant of the following 3 x 3 matrix, expanding about row 1. Solution:
If a, b and c are in harmonic progression with b as their harmonic mean then, b = This is obtained as follows. Since a, b and c are in
/3x-5/-x-7=0
all basic knowledge related to geometry
INTRODUCTION : When a child of seven isn't able to solve the sum 23+9, what could the reasons be? When she is asked to subtract 9 from 16, why does she write 9 - 16 = 13 ?
a painting is 20 cm wider than its height. its area is 2400 centimeter squared. find its lenght and width
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Six times as many people voted in the 2012 election as in the 2008 election.If 162 people voted in 2008,how many people voted in both elections?
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