The coefficient of x 9 in the expansion of 1 + x   1 + x 2   1 + x 3 … … 1 + x 100 is

Question

The coefficient of x 9 in the expansion of 1 + x &#160; 1 + x 2 &#160; 1 + x 3 &#8230; &#8230; 1 + x 100 is

Aicharya · Accepted Answer

1 + x 1 + x 2 … . ( 1 + x 100 ) Possible combination of 9 are (0, 9), (1, 8), (2, 7), (3, 6), (4, 5), (1, 2, 6), (1, 3, 5), (2, 3, 4) So, coefficient = 8.

The coefficient of x 9 in the expansion of 1 + x &#160; 1 + x 2 &#160; 1 + x 3 &#8230; &#8230; 1 + x 100 is

Solution

The coefficient of x 9 in the expansion of 1 + x 1 + x 2 1 + x 3 … … 1 + x 100 is