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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;
47x+33y=143
The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(
Nicole is forming 20 gift baskets. She has 15 pounds of chocolates to distribute equally between the baskets. If each basket gets the similar amount of chocolates, how many pounds
OTHER WAYS TO AID LEARNING : Here we shall pay particular attention to the need for repetition, learning from other children, and utilising errors for learning.
Sketch (draw) the parametric curve for the subsequent set of parametric equations. x = t 2 + t y = 2t -1 Solution At this point our simply option for sketching a par
x+2y^2=63 and 4x+y^2=0; Find the area of the regions enclosed by the lines and curves.
who discovered and when
A bucket of height 8 cm and made up of copper sheet is in the form of frustum of right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively. Calculate
How do I reverse calculate taxes?
Define Points, Lines, and Spaces Points, lines, and planes are known as undefined or primitive terms. These are the most significant and fundamental concepts in the study of geom
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