Question

(1-x+x2-........) (1+x+x2+.....)=(1+x2+x4+.....)

Answer 1

Heya User,

--> [ 1 - x + x² - .... ] <--- Infinite GP with ratio ( -x )

=> [ 1 - x + x² - .... ] = 1 / [ 1 + x ] --> ( i )

--> [ 1 + x + x² + .... ] <--- Infinite GP with ratio ( x )

=> [ 1 + x + x² + .... ] = 1 / [ 1 - x ] --> ( ii )

( i ) * ( ii ) --->

--> [ 1 - x + x² - .... ][ 1 + x + x² + .... ] = 1 / [ 1 - x² ] 

Now,  1 / [ 1 - x² ] <--- Infinite GP with ratio [ x² ]

=> [ 1 - x + x² - .... ][ 1 + x + x² + .... ] = [ 1 + x² + x⁴ + .... ] √√

Answer 2

Answer:

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Step-by-step explanation: