Home
Class 12
MATHS
Show that the middle term in the expansi...

Show that the middle term in the expansion of `(x+1)^(2n)` is `(1.3.5.....(2n-1))/(n!) 2^n.x^n`.

Text Solution

Verified by Experts

As 2n is even, the middle term of the expansion `(1+x)^(2n)` is `((2n)/(2) + 1)` th or `(n+1)` th
`T_(n+1) = .^(2n)C_(n) x^(n) = ((2n)!)/(n!n!) x^(n)`
`= (1.2.3.4"….."(2n-2)(2n-1)(2n))/(n!n!)x^(n)`
`= ([1.3.5"…."(2n-1)][2.4.6"…."(2n)])/(n!n!) x^(n)`
` = ([1.3.5"...."(2n-1)]n!)/(n!n!)2^(n).x^(n)`
` = (1.3.5"....."(2n-1))/(n!) 2^(n)x^(n)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Example|10 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.1|17 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

Show that the middle term in the expansion of (x-1/x)^(2n) is (1.3.5.7....(2n-1))/(n!)(-2)^n

Prove that the middle term in the expansion of (1+x)^(2n)" is " (1.3.5....(2n-1))/(n!).2^(n)x^(n)

Show that the value of the middle term in the expansion of (x+(1)/(2x))^(2n)" is " (1.3.5.....(2n-1))/(n!)

The middle term in the expansion of (1-3x+3x^2-x^3)^(2n) is

Determine: nth term in the expansion of (x+1/x)^(2n)

The coefficient of the middle term in the expansion of (1+x)^(2n) is

Coefficient of x^n in the expansion of (1+x)^(2n) is

The coefficient of the middle term of the expansion of (1-2x+x^2)^n is

Show that the sum of the coefficients of the odd terms in the expansion of (1+x)^(2n)" is "2^(2n-1)

Show that the sum of the coefficient of first (r+1) terms in the expansions of (1-x)^(-n) is ((n+1)(n+2)...(n+r))/(r!)