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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;
Consider a student loan of $12,500 at a fixed APR of 12% for 25 years, 1. What is the monthly payment amount? 2. What is the total payment over the term of the loan? 3. OF
A body is constrained to move in a path y = 1+ x^2 and its motion is resisted by friction. The co-efficient of friction is 0.3. The body is acted on by a force F directed towards t
Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60
y+7 3y-2 --- = 1 + ---- 3 5
Using the definition of the definite integral calculate the following. ∫ 0 2 x 2 + 1dx Solution Firstly,
Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
Rental car agency has 50 cars. Rental rate in winter is 60%. What is probability that in give winter month the rental rate is fewer than 35 cars rented? Use normal distribution to
#a invests Rs 15000IN COMPANY PAYING 10%WHEN Rs100 SHARE IS SOLD AT A PREMIUM OF Rs 20 after a yearASOLD SHARES AT Rs80 EACHAND INVESTEDPROCEEDS IN Rs75SHARES SELLING AT Rs 100 WZI
4/x+4-3/x+3=2/x+2-1/x+1
Two circles touch each other externally: Given: Two circles with respective centres C1 and C2 touch each other externaly at the point P. T is any point on the common tangent
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