60 1.8.4 Example D Find the sum of the series 1 · 2 + 2 .3+3. 4+ ...+ n(n + 1). We have k(k + 1) = (k + 1)(2); therefore, from the fundamental theorem 36 Difference Equations of the summation...

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60<br>1.8.4<br>Example D<br>Find the sum of the series 1 · 2 + 2 .3+3. 4+ ...+ n(n + 1).<br>We have k(k + 1) = (k + 1)(2); therefore, from the fundamental theorem<br>36<br>Difference Equations<br>of the summation calculus, we obtain<br>|n+1<br>E k(k +1 = >(k + 1)(2) = A-1(k + 1)(2)<br>k=1<br>k=1<br>n+1<br>= 1/3(k + 1)(3)<br>(1.268)<br>1<br>= 1/3(n + 2)(3) – 1½ · 2(3)<br>= 1/3(n + 2)(n + 1)n.<br>

Extracted text: 60 1.8.4 Example D Find the sum of the series 1 · 2 + 2 .3+3. 4+ ...+ n(n + 1). We have k(k + 1) = (k + 1)(2); therefore, from the fundamental theorem 36 Difference Equations of the summation calculus, we obtain |n+1 E k(k +1 = >(k + 1)(2) = A-1(k + 1)(2) k=1 k=1 n+1 = 1/3(k + 1)(3) (1.268) 1 = 1/3(n + 2)(3) – 1½ · 2(3) = 1/3(n + 2)(n + 1)n.

Jun 05, 2022

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60 1.8.4 Example D Find the sum of the series 1 · 2 + 2 .3+3. 4+ ...+ n(n + 1). We have k(k + 1) = (k + 1)(2); therefore, from the fundamental theorem 36 Difference Equations of the summation...

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