DISCRETE MATHS HOMEWORK QUESTIONS

Ans)
(1+x)-n = 1 – nx + (n(n+1)/2!) x2 - (n(n+1)(n+2)/3!) x3 +….
x10 term in the taylor expansion of (1-2x)-7 :
(7(7+1)(7+2)…(7+9)/10!)(-2x)10 = (16C10 2
10) x10
 Coefficient of x10 in the taylor expansion of (1-2x)-7 is (16C10 2
10)
x10 term in the taylor expansion of (1+3x)-4 :
(4(4+1)(4+2)…(4+9)/10!)(3x)10 = (13C10 3
10) x10
 Coefficient of x10 in the taylor expansion of (1+3x)-4 is (13C10 3
10)
 Coefficient of x10 in the taylor expansion of (1-2x)-7 + (1+3x)-4 is ((16C10 2
10) + (13C10 3
10))
Ans) let the first and second lines get a+1 and b+1 number of objects respectively
Since they need to get at least two objects a, b  1
let the third and fifth...