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If (e^(x))/(1-x) = B(0) +B(1)x+B(2)x^(2)...

If `(e^(x))/(1-x) = B_(0) +B_(1)x+B_(2)x^(2)+...+B_(n)x^(n)+... `, then the value of `B_(n) - B_(n-1)` is

A

1

B

1/n

C

`(1)/(n!)`

D

None of these

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If (e^(x))/(1-x) = B_(0) + B_(1)x + B_(2)x^(2) + ...+B_(n)x^(n) +... then B_(n)-B_(n-1) equals

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    `(1)/(n!)`
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  • If e^x/(1-x) =B_0 + B_1x + B_2 x^2 + cdotcdotcdot + B_n x^n +cdotcdotcdot, then B_n-B_(n-1) equals

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  • If x^(n) = a_(0) + a_(1) (1 + x) + a_(2)(1 + x)^(2) + .. .+ a_(n) (1 +x)^(n) = b_(0) + b_(1) (1 - x) + b_(2) (1 - x)^(2) + ... + b_(n)(1 - x)^(n) then for n = 201, (a_(101) , b_(101) ) is equal to:

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