IIT JEE , AIEEE Forum - Mathematics , Algebra

Sushmi

_[0]

^[1] 1 - (1- x)^n / 1 - (1-x) = [ C1x + C2 x^2/2 - C3 x^3/3 ......+(-1)^n x^n/n ]

= _[0]

^[1] {1 + (1-x) + (1-x) ^2 + ......+(1-x)^n-1 }dx

= [ x + (1-x)^2/-2 + ( 1-x)^3/-3 +.....+(1-x)^n/-n ] within limits of 0 to 1

= 1 + 1/2 + 1/3 + ......+1/n

= C1 - 1/2 C2 + 1/3 C3 - .....+(-1) ^ n-1 1/n Cn

We need the L.H.S only.

So now the problem becomes = n -[C1 - 1/2 C2 + 1/3 C3 - .....+(-1) ^n-1 1/n Cn]

Isn't it? I was speaking of this.

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