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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;
Factors in Denominator and Partial Fraction Decomposition Factor in denominator Term in partial fraction decomposition ax + b
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In this case we are going to consider differential equations in the form, y ′ + p ( x ) y = q ( x ) y n Here p(x) and q(x) are continuous functions in the
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Unit Vector and Zero Vectors Unit Vector Any vector along with magnitude of 1, that is || u → || = 1, is called a unit vector. Zero Vectors The vector w → = (
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