3. Here's a way to evaluate due to Euler. We've seen that sin 72 TZ - k² ·ÎI (¹-³). j=1 (a) Equate the coefficients of z² on both sides, to recover the desired sum. (b) Equate the coefficients of z4 on both sides to recover a different sum. By equating coefficients of higher powers of z, one can recover other identities too. On the next homework set we'll see a more general method to calculate sums.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. Here's a way to evaluate
due to Euler. We've seen that
sin 72
TZ
-
k²
·ÎI (¹-²).
j=1
(a) Equate the coefficients of z² on both sides, to recover the desired sum.
(b) Equate the coefficients of z4 on both sides to recover a different sum.
By equating coefficients of higher powers of z, one can recover other identities too.
On the next homework set we'll see a more general method to calculate sums.
Transcribed Image Text:3. Here's a way to evaluate due to Euler. We've seen that sin 72 TZ - k² ·ÎI (¹-²). j=1 (a) Equate the coefficients of z² on both sides, to recover the desired sum. (b) Equate the coefficients of z4 on both sides to recover a different sum. By equating coefficients of higher powers of z, one can recover other identities too. On the next homework set we'll see a more general method to calculate sums.
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