Oresme's proof by partitioning the harmonic series into 1 +-+ ) + 1+(2)+(3+1)+(3+2/+ has the following...

   

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Oresme's proof by partitioning the harmonic series into 1 +-+ ) + 1+(2)+(3+1)+(3+2/+ has the following geometric counterpart. y 8 0 1 2 3 4 n n+1 Figure 10.2: Comparing 1+++.... 10.1.1 By referring to Figure 10.2, show that + with an area n 1 1 1 + + 1 > area under y = between x = 1 and x = n + 1. n x Oresme's proof by partitioning the harmonic series into 1 +-+ ) + 1+(2)+(3+1)+(3+2/+ has the following geometric counterpart. y 8 0 1 2 3 4 n n+1 Figure 10.2: Comparing 1+++.... 10.1.1 By referring to Figure 10.2, show that + with an area n 1 1 1 + + 1 > area under y = between x = 1 and x = n + 1. n x