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((5)/(7))^(2)+((5)/(7))^(3x+1)=((5)/(7))...

((5)/(7))^(2)+((5)/(7))^(3x+1)=((5)/(7))^(4)

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Find the sum of each of the following infinite geometric series, if it exists : (4)/(7) - (5)/(7^(2)) + (4)/(7^(3)) - (5)/(7^(4)) + (4)/(7^(5)) - (5)/(7^(6)) +…oo

If (x)/(y)=(6)/(5), then the value of ((6)/(7)-(5x-y)/(5x+y)) is equal to (a) (1)/(7)( b) (2)/(7)(c)(3)/(7) (d) (4)/(7)

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Simplify: ((1)/(4)x(2)/(7))-((5)/(14)x(-2)/(3))+((3)/(7)x(9)/(2))

Simplify ((5^(-1)*7^(2))/(5^(2)*7^(-4)))^((7)/(2))*((5^(-2)*7^(3))/(5^(3)*7^(-5)))^(-(5)/(2))

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Verify the following: (i) ((3)/(4)+(-2)/(5))+(-7)/(10)=(3)/(4)+((-2)/(5)+(-7)/(10)) (ii) ((-7)/(11)+(2)/(-5))+(-13)/(22)=(-7)/(11)+((2)/(-5)+(-13)/(22)) (iii) -1+((-2)/(3)+(-3)/(4))=(-1+(-2)/(3))+(-3)/(4)