1.

For|x|lt(1)/(5)thecoefficientofx ^ 3intheexpansion of(1)/((1 - 5x ) ( 1 - 4 x))is

Answer»

369
370
371
372

Solution : ` (1)/(( 1 - 5 x)( 1 - 4x )) = (1 - 5x ) ^(-1) (1 - 4x ) ^( -1 ) `
`= [ 1 + 5x+(5x ) ^ 2+ (5x ) ^3 + …. ][ 1+ 4x+ (4x) ^ 2+(4x ) ^3 + … ]`
`therefore`Co- efficientof` x ^ 3` intheaboveexpansion
`= (1)(4) ^3+ 5 (4)^2 + (5 ^ 2 ) (4)+1 (5) ^ 3 `
`= 64+80+ 100 +125 `
` = 369 `


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