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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;
Question: In the interest of saving up enough money for retirement, you have created a bank account to store a sum of money. Compound interest on this account is accumulated
Price?
While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.
I need help with this question: Find the probability that two quarters and a nickel are chosen without replacement from a bag of 8 quarters and 12 nickles.
Example Reduce 24/36 to its lowest terms. 24/36=12/18=6/9=2/3. In the first step we divide the numerator and the denominator by 2. The fraction gets reduced
If tanx+secx=sqr rt 3, 0 Ans) sec 2 x=(√3-tanx) 2 1+tan 2 x=3+tan 2 x-2√3tanx 2√3tanx=2 tanx=1/√3 x=30degree
The figure shows the sketch graphs of the functions
could you help me get bater at math
(3x+2)^2 d^2y/dx^2+3(3x+2)dy/dx-36y=3x^2+4x+1
2 times n times n divided by n
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