Answer: [tex]\frac{4}{10}+\frac{4}{100}+\frac{4}{1,000}+\frac{4}{10,000}[/tex]
Step-by-step explanation:
The given geometric series are:
a)[tex]\frac{1}{4}+\frac{1}{40}+\frac{1}{400}+\frac{1}{4,000}[/tex]
on simplifying in decimals, we get
[tex]0.25+0.025+0.0025+0.00025=0.27775\neq0.4444[/tex]
b) [tex]\frac{1}{40}+\frac{1}{400}+\frac{1}{4,000}+\frac{1}{40,000}[/tex]
on simplifying in decimals, we get
[tex]0.025+0.0025+0.00025+0.000025=0.027775\neq0.4444[/tex]
c)[tex]\frac{4}{10}+\frac{4}{100}+\frac{4}{1,000}+\frac{4}{10,000}[/tex]
on simplifying in decimals, we get
[tex]0.4+0.04+0.004+0.0004=0.4444[/tex]
Thus, this geometric series represent 0.4444.
d)[tex]\frac{1}{10}+\frac{1}{100}+\frac{1}{1,000}+\frac{1}{10,000}[/tex]
on simplifying in decimals, we get
[tex]0.1+0.01+0.001+0.0001=0.1111\ \neq0.4444[/tex]
