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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;
What is Inductive Reasoning ? Sometimes we draw conclusions based on our observations. If we observe the same results again and again, we conclude that the event always has the
solve for k such that the system 4x+ky=6 kx+y=-3
Assume A and B are symmetric. Explain why the following are symmetric or not. 1) A^2 - B^2 2) (A+B)(A-B) 3) ABA 4) ABAB 5) (A^2)B
Q. Subtraction Involving Negative Numbers? In order to subtract positive and negative numbers, you need to be aware of the Rule for Subtraction. This rule states that subtracti
(3t-1)^4 (2t+1)^-4
sir/madam, i abdulla working as a maths teacher want to join ur esteemed organisation as a tutor how can i proceed i have created an account even pls guide me, thanks abdulla
At time t an investor shorts a $1 face value zero coupon bond that matures at time T = t and uses the entire proceeds to purchase a zero coupon bond that matures at time
Inverse Cosine : Now see at inverse cosine. Following is the definition for the inverse cosine. y = cos -1 x ⇔ cos y = x for
Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbles as Sam?
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