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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;
show that all primes except 2, are of the form 4n-1 or 4n+1.
Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
Why do we start dividion operation from left to right?
In this case we are going to consider differential equations in the form, y ′ + p ( x ) y = q ( x ) y n Here p(x) and q(x) are continuous functions in the
The sum of the diameters of two circles is 2.8 m and their difference of circumferences is 0.88m. Find the radii of the two circles (Ans: 77, 63) Ans: d 1 + d 2 = 2.8 m=
In this section we will consider for solving first order differential equations. The most common first order differential equation can be written as: dy/dt = f(y,t) As we wil
I am learning this at school today and I started getting confused which one is which, can you help me?
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
What was the US's policy towards Latin America during the 20th century? What were the motives behind this policy? Give one example of the US executing this policy?
Spurious Correlations - in several rare situations when plotting the data for x and y we may have a group indicating either positive correlation or negative (-ve) correlation
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