Question

32.Sa se calculeze sumele

a) 1-2+2^2-2^3+...+2^12

b)1+x+x^2+...+x^100

Answer 1

Sn = b1•(q^n -1)/(q-1)

a) 1-2+2²-2³+2⁴-2⁵+...+2^12 =

b1 = 1, n = 13, q = -2

= 1•((-2)^13-1)(-2-1) = (-2^13 -1)/(-3) =

= (2^13 +1)/3

b) 1+x+x²+...+x^100 =

b1 = 1, n = 101, q = x

= 1•(x^101-1)/(x-1) = (x^101 -1)/(x-1)