A telescoping series has the form sum(f(k)-f(k+1)), which collapses to f(1)-f(n+1). The key is recognizing or creating the telescoping structure. For rational terms: decompose using partial fractions. 1/[k(k+1)] = 1/k - 1/(k+1) → sum = 1 - 1/(n+1). For 1/[k(k+2)]: use 1/[k(k+2)] = (1/2)[1/k - 1/(k+2)] → paired telescoping. Always check the first and last few terms to identify what survives.