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Find the middle terms in the expansion of: \begin{array}{l} (i){(x - 1/x)^{10}}\\ (ii){(1 - 2x + {x^2})^n}\\ \end{array}
Binomial Theorem | CBSE | Class 11 | Exercise 18.2 | Maths | RD Sharma
Find the middle terms in the expansion of: \begin{array}{l} (i){(x - 1/x)^{10}}\\ (ii){(1 - 2x + {x^2})^n}\\ \end{array}

Answers:

(i)

Given,

(x – 1/x)10  [n = 10]

Middle term –

(n/2 + 1) = (10/2 + 1) = (5 + 1) = 6.

The term is 6th term

T6 = T5+1

RD Sharma Solutions for Class 11 Maths Chapter 18 – Binomial Theorem image - 46

Middle term is -252.

(ii) 

Given,

(1 – 2x + x2)n = (1 – x)2n  [n is an even number]

Middle term is (2n/2 + 1) = (n + 1)th term.

Tn = Tn+1

= 2nCn (-1)n (x)n

= (2n)!/(n!)2 (-1)n xn

Middle term is (2n)!/(n!)2 (-1)n xn.

i

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