Question

Buna!
Cum aflu care e rezultatul sumei Sn = 1 + 2 + 4 + ... + 2^n ?

Answer 1

[tex] Sn= 1+ 2+ 4+ .... + 2^{n} \\ Sn = 2^{0}+2^{1}+2^{2}+ .... + 2^{n} /*2\\ 2Sn= 2^{1}+2^{2} + ..... + 2^{n}+2^{n+1} \\ \\ \\ Obs. \ ca \ Sn -2^{0} = 2^{1} + 2^{2} + .... 2^{n} \rightarrow \\ 2Sn= Sn - 2^{0} + 2^{n+1}/-Sn \rightarrow Sn= 2^{n+1} - 1 [/tex]