Please solve and show yor work.  Find S25 for 1/2 + 1 + 3/2 + 2 + ...

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You should notice that adding `1/2`  to any of the terms of the sum yields the next term, hence, the terms of the sum are the terms of an arithmetic series, whose common difference is `d=1/2` .

You should remember what is the formula that helps you to evaluate the sum of n terms of arithmetic series such that:

`S_n = ((a_1 + a_n)*n)/2`

Since the number of terms is equal to 25, you need to evaluate `S_25`  such that:

`S_25 = ((1/2 + a_25)*25)/2`

`a_25 = a_1 + (25-1)*d`

`a_25 = 1/2 + 24*(1/2) => a_25 = 1/2 + 24/2 => a_25 = 25/2`

`S_25 = ((1/2 + 25/2)*25)/2 => S_25 = ((26/2)*25)/2`

`S_25 = (13*25)/2 => S_25 = 162.5`

Hence, evaluating the sum of 25 terms under the given conditions yields `S_25 = 162.5.`

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