Question

Find the coefficient of $x^{17}$ in the expansion $(x+x^2+x^3+..............x^6{)}^6(1+x+x^2+x^3+.........)$

• A. 7756
• B. 9604
• C. 3493
• D. 11914

Answer 1

The correct option is B

9604

Coefficient of $x^{17}$ in $(x+x^2+x^3+............x^6{)}^6(1+x+x^2+x^3+.........)$

Coefficient of $x^{11}$ in $(x-x^6{)}^6(1-x{)}^{-7}$

Coefficient of $x^{11}$ in $(x-6x^6{)}^6(1-x{)}^{-7}$

Coefficient of $x^{11}$ in $(1-6x^6)(1{+}^7{C}_{1}x{+}^8{C}_2{x}^2{+}^9{C}_3{x}^3+..............)$ = ${}^{17}{C}_{11}-6^{11}{C}_6{=}^{17}{C}_6-6^{11}{C}_5$