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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;
steps to trace the cartesian curve
joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the
How many ways can 4 DVDs be arranged on a shelf? Solution: There are 4 ways to choose the first DVD, 3 ways to choose the second, 2 ways to choose the third and 1 way to choo
Method of disks or the method of rings One of the simple methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation. Carrying out
I am interested in school mathematics online assignments , homework help, projects etc. I have good knowledge of mathematics and experience of 15+ years teaching mathematics in cen
Apply the concept of partial fraction and add the corresponding terms. The terms will get cut automatically leaving the first and last term
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1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase
5.6:4=x:140
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