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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;
I am comparing building a house and buying a house. which one of the option you would choose.
Write the subsequent 2nd order differential equation as a system of first order, linear differential equations. 2 y′′ - 5 y′ + y = 0 y (3) = 6 y′ (3) = -1 We can wri
TRIGONOMETRY : "The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth." Example:
what is the difference between North America''s part of the total population and Africa''s part
Explain Comparing Mixed Numbers in maths? A mixed number is made up of two parts: a whole number and a fraction. For example: 2(3/4) 2(3/4) is read "two and three-fourths
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Properties of Vector Arithmetic If v, w and u are vectors (each with the same number of components) and a and b are two numbers then we have then following properties. v →
What is Negative Exponents explain? Here's a problem which results in a negative exponent: 3 4 /3 7 = 3 (4-7) = 3 -3 A negative exponent means the same thing as making
1a.if the williams spend $385 a month on food what is their monthly income
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