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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 all the eighth roots of (19 + 7 i)
2/2
Here we know x can only be 1 or -1. so if it is 1 ans is 2. if x is -1, for n even ans will be 2 if x is -1 and n is odd ans will ne -2. so we can see evenfor negative x also an
Noah is renewing a magazine subscription. one package offers to renew the magazine for 3 years for 26$. A second package offers to renew the magazine for 5 years for $38
A sinking ship signals to the shore for assistance. Three individuals spot the signal from shore. The ?rst individual is directly perpendicular to the sinking ship and 20 meters in
3x^2+19x-14=0
(3t-1)^4 (2t+1)^-4
Correlation and Regression Correlation CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of
Multiply following and write the answers in standard form. (a) 7 i ( -5 + 2 i ) (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu
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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