Answer: 5050
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Explanation:
This series is arithmetic since the common difference is 1. In other words, we're adding 1 to each term to get the next one.
The quickest way to find the sum is to use the formula below
S = (n/2)*(a+b)
where n is the number of terms, 'a' is the first term, and b is the last (or nth) term. This formula only works for arithmetic series.
We can see that n = 100, a = 1 and b = 100, so....
S = (n/2)*(a+b)
S = (100/2)*(1+100)
S = 50*101
S = 5050
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This can be confirmed by noticing that we have 100/2 = 50 pairs of terms. Pair up the terms such that 1 goes with 100, 2 goes with 99, 3 goes with 98, and so on.
We have these fifty sums
1+100 = 101
2+99 = 101
3+98 = 101
....
48+53 = 101
49+52 = 101
50+51 = 101
We have 50 copies of 101 being added, which leads to 50*101 = 5050
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The slowest and most tedious way to confirm this is to type 1+2+3+...+98+99+100 into your calculator. The result should say 5050. Using a spreadsheet would be a better option instead of using a handheld calculator. I don't recommend this unless you need more proof that we end up with 5050 as the final answer.
