If (1 + x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + ... + C_n x^n , Prove that ΣΣ_(0≤i<j≤n) (i + j)C_i C_j = n(2^(2n−1) − (1/2)^(2n) C


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 22739 by Tinkutara last updated on 22/Oct/17

$I f {(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + C_{3} x^{3}$ $+ . . . + C_{n} x^{n},$ $P r o v e t h a t \underset{0 ⩽ i < j ⩽ n}{Σ Σ} (i + j) C_{i} C_{j} =$ $n (2^{2 n - 1} - \frac{1}{2}^{2 n} C_{n})$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum