[tex]suma \: lui \: gauss \\ 1 + 2 + ... + n = \frac{n(n + 1)}{2} \\ \\ 1 + 3 + 5 + 7 + ... + 89 \\ = (1 + 2 + 3 + ... + 90) - (2 + 4 + 6 + ... + 90) \\ = \frac{90 \times 91}{2} - 2(1 + 2 + 3 + ... + 45) \\ = \frac{8190}{2} - 2 \times ( \frac{45 \times 46}{2} ) \\ = 4095 - 45 \times 46 \\ = 4095 - 2070 \\ = 2025[/tex]
Show life that you have a thousand reasons to smile
© Copyright 2024 DOKU.TIPS - All rights reserved.
[tex]suma \: lui \: gauss \\ 1 + 2 + ... + n = \frac{n(n + 1)}{2} \\ \\ 1 + 3 + 5 + 7 + ... + 89 \\ = (1 + 2 + 3 + ... + 90) - (2 + 4 + 6 + ... + 90) \\ = \frac{90 \times 91}{2} - 2(1 + 2 + 3 + ... + 45) \\ = \frac{8190}{2} - 2 \times ( \frac{45 \times 46}{2} ) \\ = 4095 - 45 \times 46 \\ = 4095 - 2070 \\ = 2025[/tex]