Jawaban:
2016
Penjelasan dengan langkah-langkah:
[tex] {9}^{2} - {1}^{2} = (9 + 1) \times (9 - 1) = 10 \times 8[/tex]
[tex]{10}^{2} - {2}^{2} = (10 + 2) \times (10 - 2) = 12 \times 8[/tex]
[tex] {11}^{2} - {3}^{2} = (11 + 3) \times (11 - 3) = 14 \times 8[/tex]
[tex] {12}^{2} - {4}^{2} = (12 + 4) \times (12 - 4) = 16 \times 8[/tex]
[tex] {20}^{2} - {12}^{2} = (20 + 12) \times (20 - 12) = 32 \times 8[/tex]
[tex] {9}^{2} - {1}^{2} + {10}^{2} - {2}^{2} + {11}^{2} - {3}^{2} + ... + {20}^{2} - {12}^{2} \\ = 10 \times 8 + 12 \times 8 + 14 \times 8 + 16 \times 8 + ... + 32 \times 8 \\ = 8 \times (10 + 12 + 14 + 16 + ... + 32) \\ note \: dalam \: kurung \: a = 10, \: b = 2, \: dan \: c = 12 \\ = 8 \times ( \frac{n}{2} \times (a + un)) \\ = 8 \times ( \frac{12}{2} \times (10 + 32)) \\ = 8 \times 6 \times 42 \\ = 48 \times 42 \\ = 2016[/tex]
Semoga membantu ya ;)
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
Verified answer
Jawaban:
2016
Penjelasan dengan langkah-langkah:
Ingat!
a² - b² = (a+b) x (a-b)
[tex] {9}^{2} - {1}^{2} = (9 + 1) \times (9 - 1) = 10 \times 8[/tex]
[tex]{10}^{2} - {2}^{2} = (10 + 2) \times (10 - 2) = 12 \times 8[/tex]
[tex] {11}^{2} - {3}^{2} = (11 + 3) \times (11 - 3) = 14 \times 8[/tex]
[tex] {12}^{2} - {4}^{2} = (12 + 4) \times (12 - 4) = 16 \times 8[/tex]
[tex] {20}^{2} - {12}^{2} = (20 + 12) \times (20 - 12) = 32 \times 8[/tex]
Jadi
[tex] {9}^{2} - {1}^{2} + {10}^{2} - {2}^{2} + {11}^{2} - {3}^{2} + ... + {20}^{2} - {12}^{2} \\ = 10 \times 8 + 12 \times 8 + 14 \times 8 + 16 \times 8 + ... + 32 \times 8 \\ = 8 \times (10 + 12 + 14 + 16 + ... + 32) \\ note \: dalam \: kurung \: a = 10, \: b = 2, \: dan \: c = 12 \\ = 8 \times ( \frac{n}{2} \times (a + un)) \\ = 8 \times ( \frac{12}{2} \times (10 + 32)) \\ = 8 \times 6 \times 42 \\ = 48 \times 42 \\ = 2016[/tex]
Semoga membantu ya ;)