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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;
Let R be the relation on Z + defined by aRb iff gcd(a; b) = 1 (that is, a and b have no common divisors greater than one). Explain whether R is reflexive, irreflexive, symmetri
apllication in business and economics
4x-5y+16=0
what is sin, cos, and tan?
In this section we will be looking exclusively at linear second order differential equations. The most common linear second order differential equation is in the type. p (t ) y
show that the circle described on any focal chord of the parabola touches the directrix
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#a invests Rs 15000IN COMPANY PAYING 10%WHEN Rs100 SHARE IS SOLD AT A PREMIUM OF Rs 20 after a yearASOLD SHARES AT Rs80 EACHAND INVESTEDPROCEEDS IN Rs75SHARES SELLING AT Rs 100 WZI
Audrey measured the width of her dining room in inches. It is 150 inches. How many feet huge is her dining room? There are 12 inches in a foot. Divide 150 by 12 to find out the
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