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[" 15.the value of the product "],[qquad...

[" 15.the value of the product "],[qquad [6^((1)/(2))times6^((1)/(4))times6^((1)/(8))times6^((1)/(16))times..." up to infinite terms "],[" is "]]

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The value of the product 6^((1)/(2))xx6^((1)/(4))xx6^((1)/(8))xx6^((1)/(16))xx.... up to infinite terms is

3^(-1)times2^(-1)times6=

(((-2)/(3))^(-2))^(3)times((1)/(3))^(-4)times3^(-1)times(1)/(6)

(5)/(4)times(2)/(6)+(3)/(2)times(2)/(1)+(3)/(6)times(3)/(2)

The value of the infinite product 6(1)/(2)xx6^((2)/(4))xx6^((3)/(8))xx6(4)/(16)xx...

The value of the product 6(1)/(2)6(1)/(4)6(1)/(8)6(1)/(16)............ up to infinite terms

Evaluate : 5^(6)times(1)/(5^(2))times(6^(2))/(1)times(1)/(3^(2)

11(1)/(4)-:3(3)/(5)times6(2)/(3)+(1)/(6)=

(5)/(8)+(1)/(2)times((5)/(8)-(6)/(16))=