1+2C1x+3C2x2+4C3x3+…….. to ∞ terms can be summed up if

1+2C1x+3C2x2+4C3x3+…….. to ∞=(1−x)−2 is defined if |x|<1 ⇒-1<x<1

1+2C1x+3C2x2+4C3x3+…….. to ∞ terms can be summed up if

1+2C1x+3C2x2+4C3x3+…….. to ∞=(1−x)−2 is defined if |x|<1 ⇒-1<x<1

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$1 +^{2} C_{1} x +^{3} C_{2} x^{2} +^{4} C_{3} x^{3} + \dots \dots . . to \infty$ terms can be summed up if

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$x < 1$

$x > - 1$

$- 1 < x < 1$

$- \infty < x < \infty$

answer is C.

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$1 +^{2} C_{1} x +^{3} C_{2} x^{2} +^{4} C_{3} x^{3} + \dots \dots . . to \infty = (1 - x)^{- 2} is defined if | x | < 1 \Rightarrow - 1 < x < 1$

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1+2C1x+3C2x2+4C3x3+…….. to ∞ terms can be summed up if

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$1 +^{2} C_{1} x +^{3} C_{2} x^{2} +^{4} C_{3} x^{3} + \dots \dots . . to \infty$ terms can be summed up if