Question

Oblicz podaną sumę wyrazów ciągu geometrycznego

-1 - 3/2 - 9/4 - ... - 243/32

Answer 1

a1 = -1

q = -3/2 : -1 = 3/2

 

-1*3/2^(n-1) = -243/32

-3/2^(n-1) = -243/32

-3/2^(n-1) = -3/2^5

   n -1=5

   n = 6

 

S= a1+aq+aq^2....+aq^(n-1) = a1 * (1-q^n )/ (1-q)

 

S₆ = -1 * (1-(3/2)^6)/1-3/2

   = -1 * (1- 729/64 ) / -1/2

   =   -1 * (64/64 - 729/64) / -1/2

   =  -1* (-665/64) / -1/2

  =  665/64 *  (-2)=

  =  -1330/64 =

  =  -20  50/64 =

 = -20  25/ 32   <------------- odp