Sigma notation Express the following sums using sigma notation...

Question

Sigma notation Express the following sums using sigma notation. (Answers are not unique.)

(d) 1 + 1/2 + 1/3 + 1/4

Accepted Answer

Welcome back, everyone. Express the sum 2 + 1 + 2/3 + 1/2 using sigma notation. For this problem, let's find the pattern which relates the four terms. First of all, let's notice that 2 is equal to 2 divided by 1. Now, 1. is equal to 2 divided by 2, right? 2/3 can be expressed as 2 divided by 3, just as stated by the fraction itself, right? And at 1/2, well, we can already notice that we always have 2 in our numerator and our denominator increases by 1 unit. So 1/2 can be written as 2 divided by 4. This is consistent, right? 1/2 is just a simplified form of 2 divided by 4. Now let's notice that in each case, our numerator remains the same as always 2. And our denominator begins with 1 and increases by 1 unit, 123, and 4. So what we can do is simply write our sigma notation as sigma. Of our formula where basically our relationship we can write to because it's a constant divided by some variable k. And now let's understand that k represents the position of each term, right? If it's the first term, then we're dividing 2 by 1. If it's the second term, we're dividing 2 by 2 and so on. So essentially our formula is 2 divided by K, where K begins with 1. So we're introducing K equals 1 below sigma, and at the top, we want to include the final term. Since our final term is 1/2, which is represented by the 4th term, we include 4 for the upper value of the range, meaning our sigma notation is. Sigma from K equals 1 up to 4 of 2 divided by K. Thank you for watching.

Sigma notation Express the following sums using sigma notation. (Answers are not unique.)(d) 1 + 1/2 + 1/3 + 1/4

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Sigma notation Express the following sums using sigma notation. (Answers are not unique.)
(d) 1 + 1/2 + 1/3 + 1/4