Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To find the value of the series, we need to identify and sum all the terms in the given series:
[tex]\[ 1, 4, 2, 8, 3, 12, 4, 16, 5, 20, 6, 24, 7, 28, 8, 32, 9, 36, 10, 40, 11, 44, 12, 48, 13, 52, 14, 56, 15, 60, 16, 64, 17, 68, 18, 72, 19, 76, 20, 80, 21, 84, 22, 88, 23, 92, 24, 96, 25, 100. \][/tex]
### Step-by-Step Summation:
1. Identify the given numbers in the series.
2. Sum all these numbers sequentially.
Let's list and sum them step-by-step:
[tex]\[ \begin{align*} 1 + 4 &= 5, \\ 5 + 2 &= 7, \\ 7 + 8 &= 15, \\ 15 + 3 &= 18, \\ 18 + 12 &= 30, \\ 30 + 4 &= 34, \\ 34 + 16 &= 50, \\ 50 + 5 &= 55, \\ 55 + 20 &= 75, \\ 75 + 6 &= 81, \\ 81 + 24 &= 105, \\ 105 + 7 &= 112, \\ 112 + 28 &= 140, \\ 140 + 8 &= 148, \\ 148 + 32 &= 180, \\ 180 + 9 &= 189, \\ 189 + 36 &= 225, \\ 225 + 10 &= 235, \\ 235 + 40 &= 275, \\ 275 + 11 &= 286, \\ 286 + 44 &= 330, \\ 330 + 12 &= 342, \\ 342 + 48 &= 390, \\ 390 + 13 &= 403, \\ 403 + 52 &= 455, \\ 455 + 14 &= 469, \\ 469 + 56 &= 525, \\ 525 + 15 &= 540, \\ 540 + 60 &= 600, \\ 600 + 16 &= 616, \\ 616 + 64 &= 680, \\ 680 + 17 &= 697, \\ 697 + 68 &= 765, \\ 765 + 18 &= 783, \\ 783 + 72 &= 855, \\ 855 + 19 &= 874, \\ 874 + 76 &= 950, \\ 950 + 20 &= 970, \\ 970 + 80 &= 1050, \\ 1050 + 21 &= 1071, \\ 1071 + 84 &= 1155, \\ 1155 + 22 &= 1177, \\ 1177 + 88 &= 1265, \\ 1265 + 23 &= 1288, \\ 1288 + 92 &= 1380, \\ 1380 + 24 &= 1404, \\ 1404 + 96 &= 1500, \\ 1500 + 25 &= 1525, \\ 1525 + 100 &= 1625. \end{align*} \][/tex]
### Conclusion:
After summing all the terms of the series, we find that the value of the series is
[tex]\[ 1625. \][/tex]
[tex]\[ 1, 4, 2, 8, 3, 12, 4, 16, 5, 20, 6, 24, 7, 28, 8, 32, 9, 36, 10, 40, 11, 44, 12, 48, 13, 52, 14, 56, 15, 60, 16, 64, 17, 68, 18, 72, 19, 76, 20, 80, 21, 84, 22, 88, 23, 92, 24, 96, 25, 100. \][/tex]
### Step-by-Step Summation:
1. Identify the given numbers in the series.
2. Sum all these numbers sequentially.
Let's list and sum them step-by-step:
[tex]\[ \begin{align*} 1 + 4 &= 5, \\ 5 + 2 &= 7, \\ 7 + 8 &= 15, \\ 15 + 3 &= 18, \\ 18 + 12 &= 30, \\ 30 + 4 &= 34, \\ 34 + 16 &= 50, \\ 50 + 5 &= 55, \\ 55 + 20 &= 75, \\ 75 + 6 &= 81, \\ 81 + 24 &= 105, \\ 105 + 7 &= 112, \\ 112 + 28 &= 140, \\ 140 + 8 &= 148, \\ 148 + 32 &= 180, \\ 180 + 9 &= 189, \\ 189 + 36 &= 225, \\ 225 + 10 &= 235, \\ 235 + 40 &= 275, \\ 275 + 11 &= 286, \\ 286 + 44 &= 330, \\ 330 + 12 &= 342, \\ 342 + 48 &= 390, \\ 390 + 13 &= 403, \\ 403 + 52 &= 455, \\ 455 + 14 &= 469, \\ 469 + 56 &= 525, \\ 525 + 15 &= 540, \\ 540 + 60 &= 600, \\ 600 + 16 &= 616, \\ 616 + 64 &= 680, \\ 680 + 17 &= 697, \\ 697 + 68 &= 765, \\ 765 + 18 &= 783, \\ 783 + 72 &= 855, \\ 855 + 19 &= 874, \\ 874 + 76 &= 950, \\ 950 + 20 &= 970, \\ 970 + 80 &= 1050, \\ 1050 + 21 &= 1071, \\ 1071 + 84 &= 1155, \\ 1155 + 22 &= 1177, \\ 1177 + 88 &= 1265, \\ 1265 + 23 &= 1288, \\ 1288 + 92 &= 1380, \\ 1380 + 24 &= 1404, \\ 1404 + 96 &= 1500, \\ 1500 + 25 &= 1525, \\ 1525 + 100 &= 1625. \end{align*} \][/tex]
### Conclusion:
After summing all the terms of the series, we find that the value of the series is
[tex]\[ 1625. \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.