IIT JEE , AIEEE Forum - Mathematics , Algebra

sneha.bagri

SHOW THAT (C₀)²+ (C₁)²+........+ (C_n)²= (2n)!/n! n!

DON007

hey look..................

(1+ x)ⁿ= C0 + C1 x +C2 x² + C3x³+ C4x⁴+ ..........................Cn xⁿ

and also.............

(x+1)ⁿ= C0xⁿ + C1x^n-1+ C2x^n-2+...................................Cn

now mutiplying both ................

we get..................

(1+x)²ⁿ = (C0 + C1x +C2x²+................Cn xⁿ) ( C0xⁿ+ C1x^n-1+........Cn)

now the term..........

(C₀)²+ (C₁)²+........+ (C_n)²can be obtained...............................

by..................

equating hte coeficient of xⁿ............................

thus it is equal to...................

coed of xⁿ in (1+x)²ⁿ =

(2n)!/n! n!

answer.................

i m not as clear as i should be...................sorry 4 that.................

thanku