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

#title LOGIC, HOW MANY ZERO ARE THERE AT THE END OF 200

HOW MANY ZERO ARE THERE AT THE END OF 200

Geometry, #question.onstruct/draw geometric shapes with specific condition....

#question.onstruct/draw geometric shapes with specific condition.

Using a number strip substract , Another aid that can help children pract...

Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means

Precal, The law of cosines can only be applied to acute triangles. Is this ...

The law of cosines can only be applied to acute triangles. Is this true or false?

Why is vector division undefined, Division basically refers to multiplicati...

Division basically refers to multiplication of reciprocal. For example a/b is same as a*1/b or we can say, is same as a*b -1 , which is "a" multiplied to the inverse of "b". There

Calculus, how much it cost an hour

how much it cost an hour

Combining like terms, i don''t understand what my teacher when she talks ab...

i don''t understand what my teacher when she talks about when she talks about cosecutive integers etc... so can u help me???

Marketing., what is product life cycle

what is product life cycle

Linear programming, #question.As office manager of her firm, Marcellyne has...

#question.As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and hol

What was the total cost of her order, Leslie ordered a slice of pizza for $...

Leslie ordered a slice of pizza for $1.95, a salad for $2.25, and a soda for $1.05. What was the total cost of her order? The cost of every item must be added together; $1.95 +

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