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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;
Marty used the subsequent mathematical statement to show he could change an expression and still get the similar answer on both sides: 10 × (6 × 5) = (10 × 6) × 5 Which mathematica
Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r
chapter permutation & combination ex :4.6
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If ABCD isaa square of side 6 cm find area of shaded region
David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, a
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an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p
#i hve two qestion on Differential Equation i need solve it..
discuss the infinite series
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