In (x + 1) ^ 3 + (x + 1) ^ 4 + (x + 1) ^ 5 + +The coefficient of (x + 1) ^ 20 expansion with x ^ 3 term!

In (x + 1) ^ 3 + (x + 1) ^ 4 + (x + 1) ^ 5 + +The coefficient of (x + 1) ^ 20 expansion with x ^ 3 term!

Hello!
1： It can be regarded as an equal ratio sequence with common ratio (x + 1)
Sn=(x+1)^3*[1-(x+1)^18]/[1-(x+1)]
=-(x+1)^3/x+(x+1)^21/x
-(x + 1) ^ 3 / X items with x ^ 3 are 0
(x + 1) ^ 21 coefficient C21 with x ^ 4 term, 17 * x ^ 4 * 1 is 5985x ^ 4
So the coefficient is 5985
2： Because it is the coefficient of x ^ 3, the number of times must be > = 3
The sum of coefficients = c3,3 + c4,1 + c5,2 +. + c20,17
=C4,0+C4,1+C5,2+.+C20,17
= C21,17
=5985