Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method)
We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the factors, we get the term a n..
Mathematical Induction Conclusion
Conclusion - Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if (i) it holds for n = 1 and (ii) it holds for n = k+1 whenever it holds for n =..
Use binomial theorem to find the expansion of (1 - x)5
Use binomial theorem to find the expansion of (1 - x) 5 => 1 - 5x + 10x 2 - 10x 3 - 5x 4 + x 5 or 1- x + x 2 - x 3 + x 4 - x 5 or 1 - 5x + 10x 2 - 10x 3 + 5x 4 - x 5 or 1- x 5..
Theorems and Propositions
Propositions are of two kinds namely Theorem and Problems A theorem is a generalised statement, which can be proved logically. A theorem has two parts, a hypothesis, which states the given facts and a conclusion which states the property to be proved. T..
Propositions are of two kinds namely Theorem and Problems A theorem is a generalised statement, which can be proved logically. A theorem has two parts, a hypothesis, which states the given facts and a conclusion which states the property to be proved. T..Use binomial theorem to write the expansion of (1 - x)5
Use binomial theorem to write the expansion of (1 - x ) 5 => 1 - 5 x + 1 0 x 2 - 1 0 x 3 + 5 x 4 - x 5 or 1 - x + x 2 - x 3 + x 4 - x or 1 - 5 x + 1 0 x 2 - 1 0 x 3 + x 5 or None of the above..
Select the correct statement(s). I. Deductive reasoning arrives at a v..
Select the correct statement(s). I. Deductive reasoning arrives at a valid conclusion by logical reasoning based on the available facts. II. Deductive reasoning is the only method to prove theorems. III. In geometry, postulates and properties are accepted as true and these are u..
Use the binomial theorem to find the expansion. (x + y)3
Use the binomial theorem to find the expansion. ( x + y ) 3 => x 3 + 3x 2 y + 3xy 2 + y 3 or x 3 + 3x 2 y + 6xy 2 + y 3 or x 3 + x 2 y + xy 2 + y 3 or x 3 + y 3..
Use the binomial theorem to write the expansion: (x + y)3
Use the binomial theorem to write the expansion: ( x + y ) 3 => x 3 + x 2 y + x y 2 + y 3 or x 3 + 3 x 2 y + 3 x y 2 + y 3 or x 3 + 3 x 2 y + 6 x y 2 + y 3 or x 3 + y 3..
Use binomial theorem to write the expansion of (2x + 3y)3
Use binomial theorem to write the expansion of (2 x + 3 y ) 3 => 8 x 3 + 3 6 x 2 y + 5 4 x y 2 + 2 7 y 3 or 8 x 3 + 2 7 3 or x 3 + 1 8 x 2 y + 1 8 x y 2 + y 3 or 8 x 3 + 3 6 x 2 y + 3 6 x y 2 + 2 7 y 3..
Find the value of c that satisfies the conclusion of the mean value th..
Find the value of c that satisfies the conclusion of the mean value theorem for the function f ( x ) = e x in [0, 1]. => ln ( e + 1) or 1 or ln ( e - 2) or ln ( e - 1)..
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