Răspuns:
Explicație pas cu pas:
a)
S = 1/3 + 1/3^2 + 1/3^3 + 1/3^4 + 1/3^5 + 1/3^6
S/3 = 1/3^2 + 1/3^3 + 1/3^4 + 1/3^5 + 1/3^6 + 1/3^7
S - S/3 = 2S/3
2S/3 = 1/3 + 1/3^2 + 1/3^3 + 1/3^4 + 1/3^5 + 1/3^6 - 1/3^2 - 1/3^3 - 1/3^4 - 1/3^5 - 1/3^6 - 1/3^7 = 1/3 - 1/3^7
S = 3/2 *(1/3 - 1/3^7) = 1/2 - 1/2*3^6 = 1/2*(1 - 1/729) = 1/2 *728/729 = 364/729
__________
b)
S = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
S/2 = 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
S - S/2 = S/2
S/2 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128
S/2 = 1/2 - 1/128 = 64/128 - 1/128 = 63/128
S = 2* 63/128 = 63/64
