binomial theorem x y

Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has be..

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 a..

The last terms in (ii) and (iii) depends upon the fact whether n is even or odd. The binomial theorem for fractional index states that General term For r 0, T r + 1 in the expansion of (1+x) n , |x|<1,n Q is given by If x be so small that its squ..

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 zer..

Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expression suggest the conje..

The length of the line segment AB, which joins A (x 1 , y 1 ) and B (x 2 , y 2 ) is given by ..

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 + ..

Use binomial theorem to find the expansion of (2 x - y ) 4 . => 16 x 4 - 32 x 3 y + 24 x 2 y 2 - 8 xy 3 + y 4 or 16 x 4 - 32 x 3 y - 24 x 2 y 2 - 8 x..

Use binomial theorem to find the expansion of (2 x + 3 y ) 3 . => 8x 3 + 36x 2 y + 54xy 2 + 27y 3 or x 3 + 18x 2 y + 18xy 2 + y 3 or 8x 3 + 36x 2 y +..

Introduction - Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who published it in a ..