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4. Let n be a nonnegative integer. Express each sum in closed form (without or ellipsis) by using Binor Theorem or Taylor/Maclaurin series expansion: (-2)*+1 c. Σk=1k(224)

4. Let n be a nonnegative integer. Express each sum in closed form (without or ellipsis) by using Binor Theorem or Taylor/Maclaurin series expansion: (-2)*+1 c. Σk=1k(224)

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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Binomial Theorem Let a, b E IR and n be a nonnegative integer. Then, (a + b)" = [(an-k k=0 Taylor/Maclaurin Series Expansion ex k=0 00 72 k! 00 (1-x)-" = Σ(" + k-¹) xk k=0 In(1 + x) = [(-1)^ k=1 (−1)k+12 for x ER k for x € (-1,1) for x € (-1,1]
Transcribed Image Text:Binomial Theorem Let a, b E IR and n be a nonnegative integer. Then, (a + b)" = [(an-k k=0 Taylor/Maclaurin Series Expansion ex k=0 00 72 k! 00 (1-x)-" = Σ(" + k-¹) xk k=0 In(1 + x) = [(-1)^ k=1 (−1)k+12 for x ER k for x € (-1,1) for x € (-1,1]
4. Let n be a nonnegative integer. Express each sum in closed form (without or ellipsis) by using Binomial Theorem or Taylor/Maclaurin series expansion: c. Σκ=1 T(224) 00 (-2)*+1
Transcribed Image Text:4. Let n be a nonnegative integer. Express each sum in closed form (without or ellipsis) by using Binomial Theorem or Taylor/Maclaurin series expansion: c. Σκ=1 T(224) 00 (-2)*+1
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