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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Let I_n = ∫_ -1 ^1 |x| ( 1 + x + (x^2)/(2) + (x^3)/(3) + + x^ 2n 2n...

Let

I_n = \int_{-1}^1 |x| \left( 1 + x + \frac{x^2}{2} + \frac{x^3}{3} + \dots + \frac{x^{2n}}{2n} \right) dx

. If

\lim_{n \to \infty} I_n

can be expressed as rational

\frac{p}{q}

in its lowest form, then find the value of

\frac{pq(p+q)}{10}

.

Correct answer

3

Step-by-step solution

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