Example 19-5. Use the method of separation of symbols to prove the following identities : n +1 n + 1 (4) Uo + Uz + .. + U, = ( "i') Uo+("¿') auo +( "3 ') srUo + - +( ::) a-u, %3D + on (b) Uz x + Uz x² + Uz x³ + . - +aU, + ap4?U, +.. U1+ %3D (1 – x)' (1– x)3

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 32EQ
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Example 19-5. Use the method of separation of symbols to prove the following identities :
(a) Uo + U1 + ... + U, = ( "i') Uo +( "2') auo +(") a²u, + ..
n + 1
n +
N + 1
3
+ ( *:) a"
n + 1
(b) Uz x + Uz x² + Uz x³ + ..
x²
%3D
(1– x) U1 +
(1 – x)2AU1 +
(1 – x)34²U¡ + ..
|
Transcribed Image Text:Example 19-5. Use the method of separation of symbols to prove the following identities : (a) Uo + U1 + ... + U, = ( "i') Uo +( "2') auo +(") a²u, + .. n + 1 n + N + 1 3 + ( *:) a" n + 1 (b) Uz x + Uz x² + Uz x³ + .. x² %3D (1– x) U1 + (1 – x)2AU1 + (1 – x)34²U¡ + .. |
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