Question

S=1+2+2²+...+2²⁰²² VA ROG REPEDE

Answer 1

 

$\displaystyle\bf\\Explicatii:\\Formula~generala~pentru~calculul~sumelor~de~puteri\\cu~baze~egale~si~exponenti~crescatori~incepand~de~la~zero~este\!:\\\\k^0+k^1+k^2+k^3+\cdots + k^n=\frac{k^{n+1}-1}{k-1}\\\\ Rezolvare\!:\\\\1+2+2^2+\cdots +2^{2022}=\\\\=2^0+2^1+2^2+\cdots +2^{2022}=\frac{2^{(2022+1)}-1}{2-1}=\frac{2^{2023}-1}{1} =\boxed{\bf2^{2023}-1}$