The overall term \[Tr+1\] in the binomial extension is given by \[Tr+1\text{ }=\text{ }nCr\text{ }an-r\text{ }br\] Here\[a\text{ }=\text{ }1\] , \[b\text{ }=\text{ }x\] and \[n\text{ }=\text{ }m\]...
Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n – 1
The overall term \[Tr+1\] in the binomial extension is given by \[Tr+1\text{ }=\text{ }nCr\text{ }an-r\text{ }br\] The overall term for binomial \[\left( 1+x \right)2n\] is \[Tr+1\text{ }=\text{...
The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1 : 3 : 5. Find n and r
The overall term \[Tr+1\] in the binomial extension is given by \[Tr+1\text{ }=\text{ }nCr\text{ }an-r\text{ }br\] Here the binomial is \[\left( 1+x \right)n\] with\[a\text{ }=\text{ }1\] ,...
In the expansion of (1 + a)m+n, prove that coefficients of am and an are equal
We realize that the overall term \[Tr+1\] in the binomial extension is given by \[Tr+1\text{ }=\text{ }nCr\text{ }an-r\text{ }br\] Here\[n=\text{ }m+n\] , \[a\text{ }=\text{ }1\] and...
Find the middle terms in the expansions of
Find the middle terms in the expansions of
Find the 13th term in the expansion of
Find the 4th term in the expansion of
(x – 2y)12. Solution: The general term Tr+1 in the binomial expansion is given by Tr+1 = n C r an-r br Here a= x, n =12, r= 3 and b = -2y By substituting the values we get T4 = 12C3 x9 (-2y)3 =...
Write the general term in the expansion of (x2 – y x)12, x ≠ 0
The overall term \[Tr+1\] in the binomial development is given by \[Tr+1\text{ }=\text{ }n\text{ }C\text{ }r\text{ }an-r\text{ }br\] Here\[n\text{ }=\text{ }12\] , \[a=\text{ }x2\] and...
Write the general term in the expansion of (x2 – y)6
The overall term \[Tr+1\] in the binomial development is given by \[Tr+1\text{ }=\text{ }n\text{ }C\text{ }r\text{ }an-r\text{ }br\ldots \text{ }\ldots \text{ }..\text{ }\left( I \right)\]...
Find the coefficient of a5b7 in (a – 2b)12
The overall term \[Tr+1\] in the binomial extension is given by \[Tr+1\text{ }=\text{ }n\text{ }C\text{ }r\text{ }an-r\text{ }br\] Here \[a\text{ }=\text{ }a,\text{ }b\text{ }=\text{ }-\text{...
Find the coefficient of
x5 in (x + 3)8 Solution: The general term Tr+1 in the binomial expansion is given by Tr+1 = n C r an-r br Here x5 is the Tr+1 term so a= x, b = 3 and n =8 Tr+1 = 8Cr x8-r 3r…………… (i) For finding out...