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5(5)/(6)-3(8)/(9)-?...

5(5)/(6)-3(8)/(9)-?

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Q.the sum of the infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(5)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+... is

( (5)/(6)-:(6)/(7)times(6)/(7)-(8)/(9)-:1(3)/(5)+(3)/(4)times3(1)/(3)

(5)/(6) -: (6)/(7) xx ? - (8)/(9) -: 1 (2)/(5) -: (3)/(4) xx 3 (1)/(3) = 2(7)/(9)

The expression (5(5)/(8))/(6(3)/(7)) of (6(7)/(11))/(9(1)/(8))-:(8)/(9)(2(3)/(11)+(13)/(22)) of (3)/(5) equals (a) 1 (b) (1)/(2)( c) (7)/(9)( d) (5)/(12)

Simplify: (5)/(6)+(-2)/(5)-(-2)/(15) (ii) (3)/(8)-(-2)/(9)+(-5)/(36)

(iv) (6-3(1)/(8))/(5+(3)/(4+(5)/(9)))

(v) (3)/(8)+(7)/(2)+((-3)/(5))+(6)/(5)-((-9)/(8))-(3)/(2)

Simplify: (3)/(8)+(7)/(2)+(-3)/(5)+(9)/(8)+(-3)/(2)+(6)/(5)