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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;
find s10 for the arithmetic sequenxe inwhich a1=5 and a10=68
There are 20 defective bulbs in a box of 100 bulbs.if 10bulbs are choosen at random then what is the probability of there are just 3defective bulbs
A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the original number. Find the original number.
6.3/o.21
number theory trivia
Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical. Ans) 48 terms would be common to both the series... first take co
Find the sum of all natural numbers amongst first one thousand numbers which are neither divisible 2 or by 5 Ans: Sum of all natural numbers in first 1000 integers which ar
In figure, O is the centre of the Circle .AP and AQ two tangents drawn to the circle. B is a point on the tangent QA and ∠ PAB = 125 ° , Find ∠ POQ. (Ans: 125 o ) An s:
Binormal Vector - Three Dimensional Space Next, is the binormal vector. The binormal vector is illustrated to be, B → (t) = T → (t) * N → (t) Since the binormal vecto
The following graph shows the growth of the median home value in a particular region of the United States starting in 1996. The graphs starts in 1996 and shows the trend through t
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