1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 + ... + 2009^2 - 2010^2 + 2011^2 = A. 2.023.066 B. 2.033.056 C. 2.023.055 D. 2.033.066 E. 2. 033.055
Matematika
arinahasna23
Pertanyaan
1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 + ... + 2009^2 - 2010^2 + 2011^2 =
A. 2.023.066
B. 2.033.056
C. 2.023.055
D. 2.033.066
E. 2. 033.055
A. 2.023.066
B. 2.033.056
C. 2.023.055
D. 2.033.066
E. 2. 033.055
1 Jawaban
-
1. Jawaban clonofo
(1² - 2²) + (3² - 4²) + ... + (2009² - 2010²) + 2011² =
= (1+2)(1-2) + (3+4)(3-4) + ... + (2009+2010)(2009-2010) + 2011²
= -(1 + 2 + 3 + ... + 2010) + 2011²
= -(½×2010×2011) + 2011²
= 2.023.066 (A)
semoga jelas dan membantu