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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;
what does algorithm refer to
Q. Find the number of ways three letter "words" can be chosen from the alphabet if none of the letters can be repeated? Solution: There are 26 ways of choosing the first lett
(3t-1)^4 (2t+1)^-4
Absolute Convergence While we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with it as we didn't have any
Jackie invested money in two different accounts, one of that earned 12% interest per year and another that earned 15% interest per year. The amount invested at 15% was 100 more tha
PLEASE PROVIDE SOME STUFF TO WRITE ON SHARES AND DIVIDEND
Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible.
Q. Define Combined Functions? Ans. We are often interested in functions which combine a trigonometric function with another type of function. For example, y = x + sinx wi
In the riangle ABC the AB=12 cm,AC=28 cm and angle ABC=120 degrees.BC=?
Determine the Projection of b = (2, 1, -1) onto a = (1, 0, -2) There is a requirement of a dot product and the magnitude of a. a → • b → = 4 ||a
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