bigupsanky
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- 2025
guys how to do binomial proofs its so weird i dont get it.
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67 or 41it's 6 7 weekend
just gotta expand ykguys how to do binomial proofs its so weird i dont get it.
nah like prove 2n c n = so and sojust gotta expand yk
the 'given (1+x)^2n = (1+x)^n (1+x)^n'?nah like prove 2n c n = so and so
(1+X)^(2n+1) = (1+X)(1+X)^2nView attachment 48921
like this maybe?
oh ye u right ty ty(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
I didd but I cant find anyMaybe try studocu.
thsc?I didd but I cant find any![]()
they havent updated for 2025 or anything after 2021 for legal tbhthsc?
lol im not sure then ill try asking my legal peersyup
they havent updated for 2025 or anything after 2021 for legal tbh
I think they've just stopped updating the site tbh because I uploaded all my Prelim and now Trial papers for Legal and none got put on the site, same for EES.yup
they havent updated for 2025 or anything after 2021 for legal tbh