[" 12.Coefficient of "x^(29)" in the pol...

[" 12.Coefficient of "x^(29)" in the polynomial "],[qquad (x-(1)/(1times3))(x-(2)/(1times3times5))(x-(3)/(1times3times5times7))cdots....(x-(30)/(1times3times....times61))" is "]

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1+(1)/(4)+(1times3)/(4times8)+(1times3times5)/(4times8times12)=

[(1)/(4)+(1times3)/(4times8)+(1times3times5)/(4times8times12)]=

1 times 2times3+2 times 3times4+3 times 4times5+.... =?

(1)/(1times3)+(1)/(3times5)+(1)/(5times7)+(1)/(7times9)+(1)/(9times11)+(1)/(11times13)

((-4)/(3))times(1)/(2)+((-4)/(3))times((-7)/(5))

(2)/(5)times(-(3)/(7))-(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)

(2)/(5)times((-3)/(7))-(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)

[(1)/(1times2)+(1)/(2times3)+(1)/(3times4)+......+(1)/(99times100)] =

(4)/(5)times((-2)/(3))-(2)/(5)times(1)/(3)+(3)/(5)times(4)/(5)=