We know that \[\left( a\text{ }+\text{ }b \right)3\text{ }=\text{ }a3\text{ }+\text{ }3a2b\text{ }+\text{ }3ab2\text{ }+\text{ }b3\] Putting\[a\text{ }=\text{ }3x2\text{ }\And \text{ }b\text{...
Expand using Binomial Theorem
Utilizing binomial hypothesis the given articulation can be extended as Again by utilizing binomial hypothesis to grow the above terms we get From condition 1, 2 and 3 we get
Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Image 39 is √6: 1
Find an approximation of (0.99)5 using the first three terms of its expansion
\[0.99\] can be composed as \[0.99\text{ }=\text{ }1\text{ }\text{ }0.01\] Presently by applying binomial hypothesis we get \[\left( o.\text{ }99 \right)5\text{ }=\text{ }\left( 1\text{ }\text{...
Find the value of
Evaluate
Utilizing binomial hypothesis the articulation \[\left( a\text{ }+\text{ }b \right)6\] and\[\left( a\text{ }+\text{ }b \right)6\] , can be extended \[\left( a\text{ }+\text{ }b \right)6\text{...
If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer. [Hint write an = (a – b + b)n and expand]
To demonstrate that \[\left( a\text{ }\text{ }b \right)\] is a factor of\[\left( an\text{ }\text{ }bn \right)\] , it must be demonstrated that \[an\text{ }\text{ }bn\text{ }=\text{ }k\text{...
Find the coefficient of
x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem. Solution: (1 + 2x)6 = 6C0 + 6C1 (2x) + 6C2 (2x)2 + 6C3 (2x)3 + 6C4 (2x)4 + 6C5 (2x)5 + 6C6 (2x)6 = 1 + 6 (2x) + 15 (2x)2 + 20 (2x)3 + 15...
Find a if the coefficients of x2 and x3 in the expansion of (3 + a x)9 are equal
Find a, b and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively
We know that \[\left( r\text{ }+\text{ }1 \right)th\] term, \[\left( Tr+1 \right)\] , in the binomial expansion of \[\left( a\text{ }+\text{ }b \right)n\] is given by \[Tr+1\text{ }=\text{...