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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;
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
ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC. Ans: ΔAPR ∼ Δ
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1. A stack of poles has 22 poles in the bottom row, 21 poles in the next row, and so on, with 6 poles in the top row. How many poles are there in the stack? 2. In the formula N
using the formula sin A =under root 1+ cos2A /2 . find value of 30 degree, it is being given that cos 60 degree =1/2.
Let ∑ = (0, 1). Define the following language: L = {x | x contains an equal number of occurrences of 01 and 10} Either prove L is regular (by constructing a DFA/NFA or a rege
Make a file called "testtan.dat" which has 2 lines, with 3 real numbers on every line (some negative, some positive, in the range from-1 to 3). The file can be formed from the edi
how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?
6x^7-2x^3+4x-16 / 3x^2-7x+9
Wendy has 5 pairs of pants and 8 shirts. How many different combinations could she form with these items? Multiply the number of choices for each item to find out the number of
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