what-is-the-value-of-coefficient-of-x-9-in-expansion-1-x-1-x-2-1-x-3-1-x-4-1-x-100-

Question Number 93450 by john santu last updated on 13/May/20

what is the value of coefficient

of x^{9} in expansion (1 + x) (1 + x^{2})

(1 + x^{3}) (1 + x^{4}) \times \dots \times (1 + x^{100}) ?

Answered by john santu last updated on 13/May/20

Answered by mr W last updated on 13/May/20

i t i s t h e n u m b e r o f p a r t i t i o n s f r o m 9

i n t o d i s t i n c t p a r t s, w h i c h i s q (9) = 8 .

s i m i l a r l y

t h e c o e f . o f x^{5} = q (5) = 3 .

t h e c o e f . o f x^{12} = q (12) = 15 .

t h e c o e f . o f x^{50} = q (50) = 3658 .

Commented by john santu last updated on 13/May/20

what formula to get it ?

Commented by mr W last updated on 14/May/20

t h e r e i s n o c l o s e d f o r m u l a f o r q (n) .

s e e f o l l o w i n g :

Commented by mr W last updated on 14/May/20

Facebook Tweet Pin