# binomial theorem (1 Viewer)

#### Sylfiphy

##### Member
do I need to know how to prove double sigma notation and also if I do how do I learn it cuz my teacher won't teach it

#### WeiWeiMan

##### Well-Known Member
do I need to know how to prove double sigma notation and also if I do how do I learn it cuz my teacher won't teach it
what the fuck is double sigma notation

#### Average Boreduser

##### Rising Renewal
what the fuck is double sigma notation
It's when u express smn like (1+x)^3*(1+3)^8 and u can make a double sigma notation out of it bc two brakcet thingos . its not that hard tbh but very time consuming and not worth the hassle as not in syllabus iirc.

#### WeiWeiMan

##### Well-Known Member
It's when u express smn like (1+x)^3*(1+3)^8 and u can make a double sigma notation out of it bc two brakcet thingos . its not that hard tbh but very time consuming and not worth the hassle as not in syllabus iirc.
if you wanna get a single term like x^4 it seems way faster to just find certain coefficients from (1+x)^3 and multiply by the other coefficients from (1+3x)^8 or smth

sk*bidi

#### Sylfiphy

##### Member
what the fuck is double sigma notation
U tell me man idk how to prove this

#### Attachments

• 443.6 KB Views: 12

#### WeiWeiMan

##### Well-Known Member
U tell me man idk how to prove this
write it out and group it a bit

LHS = (s0+s1+s2+...+sm)(t0+t1+t2+...+tn)
= s0(t0+t1+t2+...+tn)+s1(t0+t1+t2+...+tn)+s2(t0+t1+t2+...+tn)+...+sm(t0+t1+t2+...+tn)
= s0 sigma + s1 sigma + ...+ sm sigma
= other sigma (sigma)
=RHS qed

same thought process for other case

#### liamkk112

##### Well-Known Member
U tell me man idk how to prove this
not in syllabus
for the first part, you’re showing
(s_0+s_1+s_2+…+s_m)(t_0+t_1+…+t_n)
= sum from i = 0 to m of s_i (t_0+…+t_n)
essentially
it’s pretty trivial but out of syllabus anyways, and tbh i don’t think there’s a single hsc question that would need or would be made easier with double sums