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Bossul1743
a fost răspuns

Se considera expresia E(n) = (–1)ⁿ * 2n + (-1)^n+1 * 3n , n apartine N . Calculati suma:
E(1)+E(2)+E(3)+...+E(2012).

Răspuns :

JolieJulie
Rezolvarea mai jos.........
Vezi imaginea JolieJulie
Richard76
Salut ,

Se scrie E(n) = (–1)ⁿ · 2n + (–1)ⁿ⁺¹· 3n = (–1)ⁿ · [2n + (–1) · 3n] = (–1)ⁿ · (–n). Suma devine (–1)¹ · (–1) + (–1)² · (–2) + (–1)³ · (–3) + ... + (–1)²⁰¹⁰ · (–2010) + (–1)²⁰¹¹ · (–2011) + (–1)²⁰¹² · (–2012) = 1 – 2 + 3 – 4 + ... – 2010 + 2011 – 2012 = (–1) · 1006 = –1006.

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