Differential calculus, Mathematics

Assignment Help:

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}<=n

that 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;


Related Discussions:- Differential calculus

Determine the length of the rectangle, The height of a rectangle is 20 cm. ...

The height of a rectangle is 20 cm. The diagonal is 8 cm more than the length. Determine the length of the rectangle. a. 20 b. 23 c. 22 d. 21 d. To determine the len

PROBABILITY, Find the probability of drawing a diamond card in each of the ...

Find the probability of drawing a diamond card in each of the consecutive draws from a well shuffled pack of cards,if the card drawn is not replaced after the first draw.

Objective type , when is the trnscribing process of data preparation irrele...

when is the trnscribing process of data preparation irrelevant ? a)CAPI b) mall panel c) in home interview d) all of them

Statistic, The mean height of eight children is 136cm. if the height of sev...

The mean height of eight children is 136cm. if the height of seven children are 143,125,133,140,120,135 and 152,find the height of eighth student.

Maxima and minima, Maxima and Minima We have to make a distinctio...

Maxima and Minima We have to make a distinction between relative maxima (or minima) and global maxima (or minima). Let f(x) be a function of x. Then the global maxi

#Regular Expression, Find the Regular Grammar for the following Regular Exp...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Estimate round to the nearest tenth of an inch, One inch equals 2.54 centim...

One inch equals 2.54 centimeters. The dimensions of a table made in Europe are 85 cm huge by 120 cm long. What is the width of the table in inches? Round to the nearest tenth of an

Idk, Are you suppose to divide the 1 or subtract

Are you suppose to divide the 1 or subtract

Finding the LCM, what is the LCM of 18, 56 and 104 show working

what is the LCM of 18, 56 and 104 show working

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd