Home
Class 12
MATHS
Coefficient of x^(18) in (1+x+2x^2+3x^3+...

Coefficient of `x^(18)` in `(1+x+2x^2+3x^3++18 x^(18))^2` equal to `995` b. `1005` c. `1235` d. none of these

Text Solution

Verified by Experts

Coefficient of `x^(18)` in `(1+x+2x^(2)+3x^(3)+…+18x^(18))^(2)`
=Coefficient of `x^(18)` in `(1+x+2x^(2)+3x^(3)+..+18x^(18))xx(1+x+2x^(2)+3x^(3)+..+18x^(18))`
`=1xx18+1xx17+2xx16+..+17xx1+18xx1`
`=36+(1xx17+2xx16+..+17xx1)`
`=36+sum_(r=1)^(17)r(18-r)=36+18sum_(r=1)^(17)r-sum_(r=1)^(17)r^(2)`
`=36+18(17(18))/2-(17(18)(35))/6`
=1005
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES 5.11|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES 5.12|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES 5.9|1 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Coefficient of x^(11) in the expansion of (1+3x+2x^2)^6 is equal to

Find the coefficient of x^(18) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

The coefficient of x^(17) in the expansion of (x-1)(x-2)……..(x-18) is

The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^2 b. 1 c. -2500 d. none of these

The coefficient of x^17 in the expansion of(x-1)(x-2)(x-3)….(x-18) is

lim_(xtooo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

If f(x)=1-x+x^2-x^3+. . -x^(15)+x^(16)-x^(17) , then the coefficient of x^2 in f(x-1) is a. 826 b. 816 c. 822 d. none of these

Let A = {x_1, x_2, x_3, ,x_7},B={y_1, y_2, y_3} The total number of functions f: A->B that are onto and there are exactly three element x in A such that f(x)=y_2 is equal to a. 490 b. 510 c. 630 d. none of these

The cofficient of x^(17) in the expansion of (x-1)(x-2)(x-3)….(x-18) is -

The coefficient of x^(19) in the polynomial (x-1)(x-2)(x-2^2)(x-2^(19)) is 2^(20)-2^(19) b. 1-2^(20) c. 2^(20) d. none of these