Question

Calcule a soma da série infinita:1+2/5+4/25+8/125+..)

Answer 1

$\mathsf{S=1+\frac{2}{5}+\frac{4}{25}+\frac{8}{125}+\cdots}\\\\\boxed{\mathsf{q=\frac{2}{5}}}~~~\boxed{\mathsf{a_1=1}}\\\\\mathsf{\lim S=\frac{a_1}{1-q}}\\\\\mathsf{\lim S=\frac{1}{1-\frac{2}{5}}}\\\\\mathsf{\lim S=\frac{1}{\frac{3}{5}}}\\\\\boxed{\mathsf{\lim S=\frac{5}{3}}}$