\(\int \left(1+2x+3x^{2}+4x^{3}+\cdots\r

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int \left(1+2x+3x^{2}+4x^{3}+\cdots\right)dx$ when $\left(|x|<1\right)$ is equal to

Options:

$\left(1+x\right)^{-1}+C$

$\left(1-x\right)^{-1}+C$

$\left(1+x\right)^{-2}+C$

None

Correct Answer:

$\left(1-x\right)^{-1}+C$

Explanation:

$\left(1-x\right)^{-1}=1+x+x^{2}+x^{3}+x^{4}+\cdots$