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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;
6987+746-212*7665
if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5 are in AP find x. 1/x+3 - 1/x+2 = 1/x+5-1/x+3 => 1/x 2 +5x+6 = 2/ x 2 +8x +15 => On solving we get x
Permutation - It is an order arrangement of items whether the order must be strictly observed Illustration Assume x, y and z be any of three items. Arrange these in all
WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357
Inverse Cosine : Now see at inverse cosine. Following is the definition for the inverse cosine. y = cos -1 x ⇔ cos y = x for
Bikes are on sale for 30% off the original price. What percent of the original price will the customer pay if he gets the bike at the sale price? The original price of the bike
AREAS RELATED TO CIRCLES The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. In t
Consider the following linear programming problem: Min (12x 1 +18x 2 ) X 1 + 2x 2 ≤ 40 X 1 ≤ 50 X 1 + X 2 = 40 X
(x+15)/y=10 where y=5
2feet wide and 12 feet long.tile is 2feet wide and 1.5feet long.how many tiles do I need
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