Home
Class 12
MATHS
If |x|<1, then find the coefficient of x...

If `|x|<1,` then find the coefficient of `x^n` in the expansion of `(1+2x+3x^2+4x^3+)^(1//2)dot`

Text Solution

Verified by Experts

The correct Answer is:
1
Since `1+2z+3x^(2)+4x^(3)+"……"oo= (1+x)^(2)`, we have
`(1+2x+3x^(2)+4x^(3)+"……"oo)^(1//2) = [(1-x)^(-2)]^(1//2)`
`= (1-x)^(-1)`
`= 1+x+x^(2)+"…."+x^(n) + "…."oo`
Therefore, the coefficient of `s^(n)` is `1`.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Single Correct Answer|152 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|27 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.7|9 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

If |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)|=0 , then the value of x is -

If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordered pair (A,B) is equal to

Solve the following : (i) |x-2|=(2-x) " (ii) " |x+3| = -x-3 (iii) |x^(2)-x|=x^(2)-x " (iv) " |x^(2)-x-2| =2+x-x^(2)

If f(x)=x^(2)-4x+14, g(x) = x - 1, q(x) = x - 3 and f(x) = g(x) q(x) + r(x), then find r(x).

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500

If f(x)=|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x-1)(x+1))| then the value of f(11) is -

If f(x)= |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1)):}| then find f(200) .

If f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1))| The f(100) is equal to

If f(x)= |{:(1,,x,,x+1),(2x,,x(x-1),,(x+1)x),(3x(x-1),,x(x-1)(x-2),,(x+1)x(x-1)):}| then the value of f(500) "_____"

If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value of |[x^3-1, 0, x-x^4], [0, x-x^4, x^3-1], [x-x^4, x^3-1, 0]|