Class 11 Maths Binomial Theorem Middle term

Middle term in the expansion of (a+b)n

Case 1: “n”  is even,  Total term is expansion : n+1 à Odd

Middle term = (n/2 +1)th

We Can now find the middle term using the general term formula,  Tr+1 = nCr  an–r br

Case 2: “n” is odd, total term in expansion: n+1 à Even

There will be two Middle terms = ((n+1)/2)th    &  ((n+1)/2  + 1)th terms

We can now find the middle term using the general term formula Tr+1 = nCr  an–r br

 

Numerical: Find the middle terms in the expansions of  (x/3 + 9y)10

Solution: in this case,  a= x/3, b=9y  & n = 10

Since n=10, number of terms in the expansion will be 11.

Middle terms will be (11+1)/2  = 6

To find T6, we need to put r=5 in the formula Tr+1 = nCr  an–r br

T5+1 = 10C5 (x/3)10-5 (9y)5

Or T6  = 61236x5y5

 

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