Prove that .
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Proof
(a) Prove that
(b) Prove that
(c) Let L be a real number. Prove that if , then
Deriving a Sum Derive Eulerβs famous result that was mentioned in Section 9.3, by completing each step.
(b) Prove that by using the substitution .
(c) Prove that by using the substitution .
(d) Prove the trigonometric identity
.
(e) Prove that .
(f) Use the formula for the sum of an infinite geometric series to verify that
(g) Use the change of variables
and to prove that
