Calculate

Calculate the sum of all three-digit natural numbers divisible by five.

Correct answer:

s = 98550

Step-by-step explanation:

n_{1} = 100 / 5 = 20 n_{2} = ⌊ 999 / 5 ⌋ = 199 n = n_{2} - n_{1} + 1 = 199 - 20 + 1 = 180 s_{1} = \frac{n _{1} + n _{2}}{2} \cdot n = \frac{2 0 + 1 9 9}{2} \cdot 180 = 19710 s = 5 \cdot s_{1} = 5 \cdot 19710 = 98550 Verifying Solution: s_{2} = 100 + 105 + 110 + 115 + 120 + 125 + 130 + 135 + 140 + 145 + 150 + 155 + 160 + 165 + 170 + 175 + 180 + 185 + 190 + 195 + 200 + 205 + 210 + 215 + 220 + 225 + 230 + 235 + 240 + 245 + 250 + 255 + 260 + 265 + 270 + 275 + 280 + 285 + 290 + 295 + 300 + 305 + 310 + 315 + 320 + 325 + 330 + 335 + 340 + 345 + 350 + 355 + 360 + 365 + 370 + 375 + 380 + 385 + 390 + 395 + 400 + 405 + 410 + 415 + 420 + 425 + 430 + 435 + 440 + 445 + 450 + 455 + 460 + 465 + 470 + 475 + 480 + 485 + 490 + 495 + 500 + 505 + 510 + 515 + 520 + 525 + 530 + 535 + 540 + 545 + 550 + 555 + 560 + 565 + 570 + 575 + 580 + 585 + 590 + 595 + 600 + 605 + 610 + 615 + 620 + 625 + 630 + 635 + 640 + 645 + 650 + 655 + 660 + 665 + 670 + 675 + 680 + 685 + 690 + 695 + 700 + 705 + 710 + 715 + 720 + 725 + 730 + 735 + 740 + 745 + 750 + 755 + 760 + 765 + 770 + 775 + 780 + 785 + 790 + 795 + 800 + 805 + 810 + 815 + 820 + 825 + 830 + 835 + 840 + 845 + 850 + 855 + 860 + 865 + 870 + 875 + 880 + 885 + 890 + 895 + 900 + 905 + 910 + 915 + 920 + 925 + 930 + 935 + 940 + 945 + 950 + 955 + 960 + 965 + 970 + 975 + 980 + 985 + 990 + 995 = 98550

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You need to know the following knowledge to solve this word math problem:

Level of the problem:

high school

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