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Question Number 147453 by EDWIN88 last updated on 21/Jul/21

 (1−(1/4))(1−(1/9))(1−(1/(16)))(1−(1/(25)))...=?

$$\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{9}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{16}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{25}}\right)...=? \\ $$

Commented by gsk2684 last updated on 21/Jul/21

 (1−(1/4))(1−(1/9))(1−(1/(16)))(1−(1/(25)))...=?  (1−(1/2))(1+(1/2))(1−(1/3))(1+(1/3))(1−(1/4))(1+(1/4))...  (1/2) (3/2) (2/3) (4/3) (3/4) (5/4) ...  (1/2)

$$\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{9}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{16}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{25}}\right)...=? \\ $$$$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\right)... \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:\frac{\mathrm{3}}{\mathrm{2}}\:\frac{\mathrm{2}}{\mathrm{3}}\:\frac{\mathrm{4}}{\mathrm{3}}\:\frac{\mathrm{3}}{\mathrm{4}}\:\frac{\mathrm{5}}{\mathrm{4}}\:... \\ $$$$\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Commented by puissant last updated on 21/Jul/21

nice sir gsk..

$${nice}\:{sir}\:{gsk}.. \\ $$

Answered by liberty last updated on 21/Jul/21

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