lim ⁡ x → ∞ ( ∑ k = 1 48 x 2 ( k x + 1 ) ( k x + x + 1 ) ) \lim_{x \to \infty} \left(\sum_{k=1}^{48}\frac{x^2}{(kx+1)(kx+x+1)}\right)

Algebra Level 2

What is the value of the limit lim ⁡ x → ∞ ( ∑ k = 1 48 x 2 ( k x + 1 ) ( k x + x + 1 ) ) ? \lim_{x \to \infty} \left(\sum_{k=1}^{48}\frac{x^2}{(kx+1)(kx+x+1)}\right)?

1 47 49 \frac{47}{49} 48 49 \frac{48}{49} 6 7 \frac{6}{7}

Ajay Dutta by Ajay Dutta , 24, India

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1 solution

first take limit . ans comes 1/k(k+1). then break 1/k-1/(k+1). now take sigma

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