• Best of luck to the class of 2025 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here

Class of 2025 (2025 HSC CHAT) (28 Viewers)

alphxreturns

alphxreturns

Well-Known Member
Joined
Oct 22, 2024
Messages
649
Gender
Male
HSC
2025
bigupsanky said:
nah like prove 2n c n = so and so
Click to expand...
the 'given (1+x)^2n = (1+x)^n (1+x)^n'?

look for coefficients, look for substitutions for x, look for anything thats recognisable from either lhs or rhs. like derivatives or integrals
 
alphxreturns

alphxreturns

Well-Known Member
Joined
Oct 22, 2024
Messages
649
Gender
Male
HSC
2025
bigupsanky said:
View attachment 48921
like this maybe?
Click to expand...
(1+X)^(2n+1) = (1+X)(1+X)^2n

expanding LHS

(2n+1)C0 × X^0 + (2n+1)C1 × X^1 + ... + (2n+1)Cn × X^n + ... + (2n+1)C(2n+1) × X^2n+1

symmetry of Pascal's triangle means nC0 = nCn
and so on, (2n+1)C0 = (2n+1)C(2n+1)

so since 2n+1 is odd, (sub n = any number if u want proof)
letting X = 1,
the expansion is 2((2n+1)C0 + ... + (2n+1)Cn)
rhs = (1+1)(1+1)^2n

so 2n+1C0 +...+ 2n+1Cn = 4^n

sorry I'm pressed on time but the main part was symmetry and X=1
 
R

ros545

New Member
Joined
Nov 11, 2024
Messages
18
Gender
Undisclosed
HSC
2022
Hey, is early entry for UTS closing today at 11:59pm (7th September) or tomorrow at 11:59pm (8th September)?
Thanks
 
bigupsanky

bigupsanky

Well-Known Member
Joined
Jul 1, 2025
Messages
784
Gender
Male
HSC
2025
alphxreturns said:
(1+X)^(2n+1) = (1+X)(1+X)^2n

expanding LHS

(2n+1)C0 × X^0 + (2n+1)C1 × X^1 + ... + (2n+1)Cn × X^n + ... + (2n+1)C(2n+1) × X^2n+1

symmetry of Pascal's triangle means nC0 = nCn
and so on, (2n+1)C0 = (2n+1)C(2n+1)

so since 2n+1 is odd, (sub n = any number if u want proof)
letting X = 1,
the expansion is 2((2n+1)C0 + ... + (2n+1)Cn)
rhs = (1+1)(1+1)^2n

so 2n+1C0 +...+ 2n+1Cn = 4^n

sorry I'm pressed on time but the main part was symmetry and X=1
Click to expand...
oh ye u right ty ty
 
M

mookie9882882

Member
Joined
Jul 25, 2025
Messages
25
Gender
Female
HSC
2025
guys i need good pen recs my handwriting is shit and i need a pen thats not too inky but also really good
 
You must log in or register to reply here.

Users Who Are Viewing This Thread (Users: 4, Guests: 24)

  • ... and 3 more.
    • Top