268 INTEGRATION 12 + 22 + 32 +.. + n2 lim 32. 3 12 n → +% 5 k n-1 2k2 33. lim 34. lim ,2 12 +* k3D1 3 n- +* k=1 Σ (:-) 35. lim n - +x n. in k=1 36. Show that 1.2+2.3+ .+ n(n + 1) = žn(n + %3D 37. Show...

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Extracted text: 268 INTEGRATION 12 + 22 + 32 +.. + n2 lim 32. 3 12 n → +% 5 k n-1 2k2 33. lim 34. lim ,2 12 +* k3D1 3 n- +* k=1 Σ (:-) 35. lim n - +x n. in k=1 36. Show that 1.2+2.3+ .+ n(n + 1) = žn(n + %3D 37. Show that the sum of the first n consecutive p- integers is n2. When each term of a sum cancels part of the n leaving only portions of the first and last terms at th sum is said to telescope. In Exercises 38-43, eva telescoping sum. V. 50 38. 39. (3k - 3k- k k = 1 k + 1 k7 | 20 (1 100