Question-68611

Question Number 68611 by TawaTawa last updated on 14/Sep/19

Answered by mind is power last updated on 15/Sep/19

\frac{1}{r^{2} - 4} = \frac{1}{4 (r - 2)} - \frac{1}{4 (r + 2)}

\Rightarrow \sum_{r = 3}^{100} \frac{1}{r^{2} - 4} = \frac{1}{4} Σ (\frac{1}{r - 2} - \frac{1}{r + 2}) = \frac{1}{4} (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} - \frac{1}{99} - \frac{1}{100} - \frac{1}{101} - \frac{1}{102})

x = 25 (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} - \frac{1}{99} - \frac{1}{100} - \frac{1}{101} - \frac{1}{102}) = 51.088 \dots .

[x] = 51

Commented by TawaTawa last updated on 17/Sep/19

God bless you sir