Binomial Theorem, Exponential and Logarithmic Series



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(7) Find the middle term in the expansion of (2a +3x)³⁰.
Solution
Here,the number of terms inthe expansion of (2a+3x)³⁰ is 30+1 i.e. 31.So, there is only one middle term.
middle term=

=C(30,15) (2a)²⁰⁻¹⁵ . (3x)¹⁵
=C(30,15) (2a)¹⁵ .(3x)¹⁵
=30!/(15!)² (2a)¹⁵ .(3x)¹⁵

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