An introduction to the Smarandache Square

... Case 1. According to the theorem 7 Ssc(n)=n and Ssc(n+1)=n+1 that implies that Ssc(n)<>Ssc(n+1) Case 2. Without loss of generality let's suppose that: n = pa ⋅ q b n + 1 = p a ⋅ qb + 1 = sc ⋅ t d where p,q,s and t are distinct primes. According to the theorem 4: Ssc( n) = Ssc ( p a ⋅ q b ) = p odd ( ...

... Case 1. According to the theorem 7 Ssc(n)=n and Ssc(n+1)=n+1 that implies that Ssc(n)<>Ssc(n+1) Case 2. Without loss of generality let's suppose that: n = pa ⋅ q b n + 1 = p a ⋅ qb + 1 = sc ⋅ t d where p,q,s and t are distinct primes. According to the theorem 4: Ssc( n) = Ssc ( p a ⋅ q b ) = p odd ( ...

Elementary Real Analysis - ClassicalRealAnalysis.info

... have opted for the user-friendly approach. We feel this approach makes the concepts more meaningful to the student. Our experience with students at various levels has shown that most students have difficulties when topics that are entirely new to them first appear. For some students that might occur ...

... have opted for the user-friendly approach. We feel this approach makes the concepts more meaningful to the student. Our experience with students at various levels has shown that most students have difficulties when topics that are entirely new to them first appear. For some students that might occur ...

451 sample Questions 2

... 31)=?a simle calcutation 23. x/2y=2a,then 2x/x2ay=?(some thing like this .very easy ) 24. A big Question describing a story.After that a number is given eg 2880.by what if we divide the number it ll become a perfect square?Ans:5 25. 1st a story. Then a simple ratio problem. The question was if the r ...

... 31)=?a simle calcutation 23. x/2y=2a,then 2x/x2ay=?(some thing like this .very easy ) 24. A big Question describing a story.After that a number is given eg 2880.by what if we divide the number it ll become a perfect square?Ans:5 25. 1st a story. Then a simple ratio problem. The question was if the r ...

File

... 22. (40*40* 40-31*31*31)/(40*40+40*31+31*31)=?a simle calcutation 23. x/2y=2a,then 2x/x-2ay=?(some thing like this .very easy ) ...

... 22. (40*40* 40-31*31*31)/(40*40+40*31+31*31)=?a simle calcutation 23. x/2y=2a,then 2x/x-2ay=?(some thing like this .very easy ) ...

... and generalised non-crossing partitions, plus several new ones; see Corollaries 12, 14, 16–19 and the accompanying remarks. Section 9 presents the announced computational proof of the F = M (ex-)Conjecture for type Dn , based on our formula in Corollary 19 for the rank-selected chain enumeration in ...

Untitled

... fractions. These positive and negative numbers, together with zero, are called the rational numbers. Hence, a rational number is defined to be any number that can be expressed as the quotient, or ratio, of two integers. For example, 2/3, 5 (which may be considered as 5/1), and 7 are rational numbers ...

... fractions. These positive and negative numbers, together with zero, are called the rational numbers. Hence, a rational number is defined to be any number that can be expressed as the quotient, or ratio, of two integers. For example, 2/3, 5 (which may be considered as 5/1), and 7 are rational numbers ...

Preparation from Question Banks and Practice... School level Quiz Competition

... Perimeter of the top of a table in the conference hall is 32cm. If the length of the table is 3 times its breadth, how long is the table? ...

... Perimeter of the top of a table in the conference hall is 32cm. If the length of the table is 3 times its breadth, how long is the table? ...

# Law of large numbers

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)