Plane trigonometry, by S.L. Loney.

[Exs. LXV.] INFINITE PRODUCTS. EXAMPLES.

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24. An infinite straight line is divided by an infinite number of points
into portions each of length a. If any point P be taken so that y is its
distance from the straight line and x is its distance measured along the
straight line from one of the points of division, prove that the sum of the
squares of the reciprocals of the distances of the point P from all the
points of division is
27ry
sinh -
a
ay cosh 2ry os 2rx
cosh — - cosa a
[Use the result of Ex. 7.]
25. If a, b, c...... denote all the prime numbers 2, 3, 5...... prove that
(a1 +)( 1 )(1.......
(and + 1+ 15
and ~ ~~~ ~ ~~~ Thr2 ~~j\t~""'=

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