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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;
( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5 4bx- 2by = - 1
the sum of the interior angles of a convex rectilinear figure is equal to sum of the exterior angles. then the number of sides is
a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p
assignment for appications of derivatives
If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0
What are the Basic Elements of Reasoning ? There are four basic elements used in geometry. If we say studying geometry is like building a house, then these elements are like d
wha is intergration?
If a country with a struggling economy is losing the battle of the marketplace, should the affected government adjust its trade barriers to tilt the economic advantage of its domes
Evaluate: 30 - 12÷3×2 =
1. Four different written driving tests are administered by a city. One of these tests is selected at random for each applicant for a drivers license. If a group of 2 women and 4 m
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