Настенно-потолочный светильник General GCF-14-IP65-RS-6-P 437544

+ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55. What is the sum of the integers from 1 to 100? Let S be the sum of the integers from 1 to 100. S = 1 + 2 + 3 + ... + 99 + 100. We can use the formula for the sum of an arithmetic series: S = n/2 * (a1 + an) where: n is the number of terms a1 is the first term an is the last term In this case: n = 100 (there are 100 integers from 1 to 100) a1 = 1 (the first integer) an = 100 (the last integer) Substitute these values into the formula: S = 100/2 * (1 + 100) S = 50 * (101) S = 5050 So, the sum of the integers from 1 to 100 is 5050. Another way to think about it (Gauss's method): Write the sum forwards and backwards: S = 1 + 2 + 3 + ... + 98 + 99 + 100 S = 100 + 99 + 98 + ... + 3 + 2 + 1 ---------------------------------------------- 2S = 101 + 101 + 101 + ... + 101 + 101 + 101 There are 100 pairs, and each pair sums to 101. 2S = 100 * 101 2S = 10100 S = 10100 / 2 S = 5050 The final answer is $5050}$.