Binomial Theorem y Página india

Prove that following (Cr = nCr)

(a) C1 + 2C2 + 3C3 + ………. n Cn = n* 2^(n–1)

(b) C1 – 2C2 + 3C3 + – ……… = 0(c) C0 + 2C1 + 3C2 +…….. + (n + 1) Cn = (n + 2) 2^(n–1)

Example : 27 (En los números complejos)

If S1 = nC0 + nC3 + nC6 + …………

S2 = nC1 + nC2 + nC7 + …………S

3 = nC2 + nC5 + nC8 + …………

each series being continued as far as possible, show that the values of S1 , S2 and S3

are 1/3(2n + 2 cos rπ/3) where r = n1 n – 2, n + 2 respectively and n ∈ N.

 

Esto sale de la Pagina india que es realmente impresionante:

http://www.mathematicsonline.co.in/iitjee.htm

~ por leonsotelo en Marzo 31, 2008.