@smsubham I didn't get "Terms beyond x^6 we cannot use to get x^12 here.".

and why are you using three terms? Why not (x^3)*(x^9) to get (x^12)?

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51 votes

@smsubham I didn't get "Terms beyond x^6 we cannot use to get x^12 here.".

and why are you using three terms? Why not (x^3)*(x^9) to get (x^12)?

0

0

7 votes

= [ x^{3 }( 1 + x + x^{2 }+ x^{3 }+ ....................... ) ]^{3}

= x^{9 }( 1 + x + x^{2 }+ x^{3 }+.......................)^{3}

= x^{9 }(1 / ( 1 - x ) )^{3}

= x^{9 }( 1 / ( 1 - x )^{3 })

= x^{9 }( ( 1 - x )^{-3 })

= x^{9 }( 1 + (3)x + ( (3*4) / (1*2) ) x^{2 }+ ( (3*4*5) / (1*2*3) ) x^{3 }+...................................)

= x^{9 }+ 3x^{10 }+ 6x^{11 }+ 10x^{12 }+........................................................

Answer = 10