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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;
Consider the function f(x) =1/2 (2 x +2 -x ) which has the graph (a) Explain why f has no inverse function. You should include an example to support your explanation
Need help, please anybody solve this: Consider the universal set T and its subsets A, B and C underneath as: T = {a, b, c, d e, f} A = {a, d} B = {b, c, f} C = {a, c
What is the largest number (in decimal) that can be made with 6 bits?
The base and corresponding altitude of a parallelogram are 10 cm and 12 cm reap. If the other altitude is 8 cm , find the length of the other pair of parallel side
Given So calculate AB. Solution The new matrix will contain size 2 x 4. The entry in row 1 and column 1 of the new matrix will be determined by multiplying row 1 of
Joe took out a car loan for $12,000. He paid $4,800 in interest at a rate of 8% per year. How many years will it take him to pay off the loan? Using the easy interest formula I
Dawn wants to evaluate the volume of a basketball along with the volume of a tennis ball. Which formula will she use? The volume of a sphere is 4/3 times π times the radius cub
what is a perfect square
Linear Equations We'll begin the solving portion of this chapter by solving linear equations. Standard form of a linear equation: A linear equation is any equation whi
what is harmonic progression
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