Question

Find the coefficient of $x^{15}$ in $(x^3+x^6+x^9+...........)(x^2+x^4+x^6+...........)(x+x^2+x^3+..........)$

• A. 10
• B. 15
• C. 12
• D. 20

Answer 1

The correct option is B

15

Number of solution is equal to coefficient of $x^{15}$ in

$(x^3+x^6+x^9+.............)(x^2+x^4+x^6+...................)(x+x^2+x^3+..................)$

= Coefficient of $x^9$ in $(1+x^3+x^6+x^9)(1+x^2+x^4+........x^8)(1+x+x^2+x^3+...........x^9)$

Neglecting higher powers

Coefficient of $x^9$ in $(1+x+x^2+x^3+..............x^9)(1+x^2+x^3+x^4+x^5+2x^6+x^7+2x^8+2x^9)$

= 1 + 1 + 1 + 1 + 1 + 2 + 1 + 2 + 2 = 12

So, number of ways = 12