fractional index


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General Term for Fractional Index
The General Term for Fractional Index is:..
Binomial Theorem for Fractional Index
Binomial Theorem for Fractional Index - For any rational number n, We accept this expansion without proof. The restriction on x is not required when n is a natural number. Now, we shall see that when n is a natural number, then the above expansion coincides with that as given ea..
Expansions for Fractional Index
Some particular expansions for Fractional Index - For n Q, we hav..
Binomial Theorem for Fractional Index
For any rational number n, We accept this expansion without proo..
Particular Terms for Fractional Index
Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (1+x) n . This can be done by expanding (1+x) n to certain terms and then locating the required term. Generally this becomes a tedious task. In such cases, we begin by evaluating the ..
General Term for Fractional Index
For n Q and |x|<1, we have ...
Some Applications of Binomial Theorem for Fractional Index
If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all approximately zero..
Petroleum fractions Animation
Learn through Animation Nuclear Fission and Fusion..
Indices
If m is a positive integer, a x a x a .. m times is written as am. a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a..
Indices and laws of indices
Indices - If m is a positive integer, a x a x a .. m times is written as am. a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it ..
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