Browse Questions

Find the sum of the series 1, $\frac {7}{5}$, $\frac {13}{25}$, $\frac {19}{25}$,----,$\infty$.

$(a)\;16/25\qquad(b)\;2\qquad(c)\;25/8\qquad(d)\;\infty$

Explanation:
$Let S=1+7/5+13/25+19/125--------\infty$
Divide by 5
S/5=1/5+7/25+13/125+----------$\infty$
Subtracting
S-S/5=4S/5=1+(7/5-1/5)+(13/25-7/25)+19/25-13/125------$\infty$
4S/5=1+6/5+6/25+6/125+6/625+-------$\infty$
4S/5=1+6(1/5+1/25+1/125+------$\infty$)
$\frac{4S}{5}=1+6(\frac{1/5}{1-1/5})\qquad(As\; the\; term\; is\; GP,S_\infty=\frac{a}{1-r} )$
4S/5=1+6*1/4=5/2
S=5/2*5/4=25/8.