Special series and telescoping sums
Sequences, series and the binomial theorem · Mathematics
Study notes
Q: Find the sum: 1/(1x2) + 1/(2x3) + ... + 1/(9x10). Step 1: Split each: 1/(kx(k+1)) = 1/k - 1/(k+1). Step 2: Sum = (1 - 1/2) + (1/2 - 1/3) + ... + (1/9 - 1/10). Step 3: Middle terms cancel (telescope): = 1 - 1/10 = 9/10.