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The coefficient of k-1 in 1+x (1-2x)5

The coefficient of k-1 in 1+x (1-2x)5

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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EXERCISES 7.2.7. Calculate the following. 2) The coefficient of x4 in (1-x)-². 3) The coefficient of an in (1+x)-4. 4) The coefficient of x-1 in = 1+x (1-2x)5 [Hint: Notice that (1-2x)-5+ (1 - 2r)-5. Work out the coefficient of an in (1-2x)-5 and in x(1-2x)-5, substitute n = k-1, and add the two coefficients.] 5) The coefficient of rk in 1/(1-¹)", where j and n are fixed positive integers. [Hint: Think about what conditions will make this coefficient zero.] 200
Transcribed Image Text:EXERCISES 7.2.7. Calculate the following. 2) The coefficient of x4 in (1-x)-². 3) The coefficient of an in (1+x)-4. 4) The coefficient of x-1 in = 1+x (1-2x)5 [Hint: Notice that (1-2x)-5+ (1 - 2r)-5. Work out the coefficient of an in (1-2x)-5 and in x(1-2x)-5, substitute n = k-1, and add the two coefficients.] 5) The coefficient of rk in 1/(1-¹)", where j and n are fixed positive integers. [Hint: Think about what conditions will make this coefficient zero.] 200
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