It is even not known whether y is rational or irrational, though conjectured to be transcendental. Hence it is desirable

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It Is Even Not Known Whether Y Is Rational Or Irrational Though Conjectured To Be Transcendental Hence It Is Desirable 1 (56.29 KiB) Viewed 39 times

It is even not known whether y is rational or irrational, though conjectured to be transcendental. Hence it is desirable to approximate y by rational numbers. Hilbert mentioned that the irrationality of y is an unsolved problem that seems unapproachable. Nowadays the numerical value of y is computed to more than 100 million decimal places. Papanikolaou pointed out that, if y were rational, then the denominator would have at least 242080 digits. Improbable! Question: 2.11 Making use of the formula show that sin (2n + 1)0 (2n + 1) sin 0 holds for all real x. sin лx TX n k=1 1- sin²0 sin² kr/(2n + 1), -(¹-²) n=1