Question

Fie E(n)=(-1)^n,unde n€N.Calculati suma :S=E(0)+E(1)+E(2)+....E(1998)​

Answer 1

$E(n) = {( - 1)}^{n} \: \: \: ,n\:\in\:\mathbb{N}$

$S=E(0)+E(1)+E(2)+E(3)+...+E(1997)+E(1998)$

$S = {( - 1)}^{0} + {( - 1)}^{1} + {( - 1)}^{2} + {( - 1)}^{3} + ... + {( - 1)}^{1997} + {( - 1)}^{1998}$

$S = 1 - 1 + 1 - 1 +... - 1 + 1$

$S = 0 + 0 + ... + 0 \: (1998 \div 2 = 999 \: ori)$

$S = 0 \times 999$

$S = 0$