\frac{1}{k(k+1)} = \frac{A}{k} + \frac{B}{k+1}
Related Articles
- = 16 - 40 + 24
- Question:** A mathematician is analyzing a topological space and needs to compute the sum of the series \( \sum_{k=1}^{50} \frac{1}{k(k+1)} \) as part of a homology calculation. Calculate this sum.
- Solution:** The given series is \( \sum_{k=1}^{50} \frac{1}{k(k+1)} \). We can simplify the terms using partial fraction decomposition:
- Solving \( 1 = A(k+1) + Bk \), we equate coefficients:
- \( A + B = 0 \)
- \( A = 1 \)
Trending Articles
Power Platform Admin Secrets: Unlock Hidden Features That Transform Your Workflow!
Top-Account Power Platform Admin Tips You Wont Find Anywhere Else!
Power Platform Admin Deal: How to Elevate Your Management Game Instantly!
A theater sells tickets for a show at $15 each. If a group of 8 friends buys tickets together and receives a 10% group discount on the total price, how much do they pay in total?
Total cost with discount = $120 - $12 = $108
A car travels 150 miles using 5 gallons of fuel. If the car continues at the same fuel efficiency, how
What Is PowerPoint? The Shocking Truth Every Professional Should Know!
PowerPoint What Is? The Secret Hack Youre Not Using (And Will Regret Missing!)
PowerPoint What Is? The Surprising Answer That Will Transform Your Presentations!
PowerPoint What Is? The Hidden Features That Make Your Slides Go From Boring to Brilliant!