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a) Using the Difference Taylor Theorem find the constants ao, a1, a2, 03 such that *-- () - - () -- () +() + a1 + a2 + a3 b) Use your answer in (a) and the Hockey Stick Identity to find an explicit formula for 1*+2* +3* +• · ·+n*. Leave the answer as a linear combination of binomials.

a) Using the Difference Taylor Theorem find the constants ao, a1, a2, 03 such that *-- () - - () -- () +() + a1 + a2 + a3 b) Use your answer in (a) and the Hockey Stick Identity to find an explicit formula for 1*+2* +3* +• · ·+n*. Leave the answer as a linear combination of binomials.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Using the Difference Taylor Theorem find the constants ao, a1, a2, a3 such that + a1 + az 5) + a3 (40 (b) Use your answer in (a) and the Hockey Stick Identity to find an explicit formula for 13+2* + 3* +• · +n³. Leave the answer as a linear combination of binomials.
Transcribed Image Text:(a) Using the Difference Taylor Theorem find the constants ao, a1, a2, a3 such that + a1 + az 5) + a3 (40 (b) Use your answer in (a) and the Hockey Stick Identity to find an explicit formula for 13+2* + 3* +• · +n³. Leave the answer as a linear combination of binomials.
Expert Solution
Step 1

Explanation

(a)

Given that 

x3=a0x0+a1x1+a2x2+a3x3

To Find - by using the Taylor Theorem we have to find the constants a0, a1, a2 , a3

as we know

nr=n!(n-r)!r!

steps

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