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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;
if oranges are bought at the rate of 11 for rupees 10 and are sold at the rate of 10 for rupees 11, find the profit percent
Evaluate following limits. Solution Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the fol
2 1/3
if b+c=3a then the value of cotB/2.cotC/2 is equal to
how do you add all the Y.AND X UP WITH 3
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
This problem involves the question of computing change for a given coin system. A coin system is defined to be a sequence of coin values v1 (a) Let c ≥ 2 be an integer constant
Two planes leave the airport at the similar time. Minutes later, plane A is 70 miles due north of the airport and plane B is 168 miles due east of the airport. Determine the distan
What is the formulate of finding commission
Five years ago a business borrowed $100,000 agreeing to repay the principal and all accumulated interest at 8% pa compounded quarterly, 8 years from the loan date. Two years after
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