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please answer both questions from your own work on a paper providing all steps for good feedback. 3. Show that the given series is convergent

please answer both questions from your own work on a paper providing all steps for good feedback.

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3. Show that the given series is convergent and nd its sum. [X1 Eran1+1) n=1 4. One of the most important innite series is the harmonic series. i11+1+1+1+1+ 111 2 3 4 5 11: Use the following steps to determine whether the harmonic series is convergent or divergent 3) bl 11] Write out the partial sums s1. s2, s4 and SE in a column. [You don't have to add the terms.) Write the following expressions in a second column. 1 1+1 1+1+1+1 1+1+1+1+1+1+1+1 2 2 4- 4 2 4 4 8 8 8 8 Compare each expression with the corresponding expression in the opposite column using equal signs or inequality symbols. Imagine if we continued these patterns. For example. the next expression in each colunm would be as follows. 1+1+1+1+1+1+1+1+1+ 1 + 1 + 1 + 1 + 1 + 1 + 1 2 3 4 5 s T a 9 10 11 12 13 14 15 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1++E+E+E+E+E+E+E+E+E+E+E+E+E+E As these numerical patterns continue, what pattern of equal signs or inequality symbols would we see? Use this to make an argument why the harmonic series is convergent or divergent

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