MKM INTEG

$\mathop{\lim}\limits_{n \to \infty}[ \frac{1}{3n^2 + 8n + 4 }+ \frac{1}{3n^2 + 16n + 16 }+ .......+ to, n, terms ]$

for PRACTICE

#Mathematics #Calculus

2 Answers

The series is like...3n^{2} + 8rn + 4r^{2}

3n^{2} + 8rn + 4r^{2} = 3n^{2} + 6rn + 2rn + 4r^{2} = (3n + 2r)(n + 2r)

so take r/n = x and 1/n = dx...so the summation reduces to

\int_{0}^{1}}{\frac{dx}{(3 + 2x)(1 + 2x)}

which can be easily solved by using partial fractions...

PERFECT GOVIND BHAI

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