Answer: \(\frac{4}{10}+\frac{4}{100}+\frac{4}{1,000}+\frac{4}{10,000}\)
Step-by-step explanation:
The given geometric series are:
a)\(\frac{1}{4}+\frac{1}{40}+\frac{1}{400}+\frac{1}{4,000}\)
on simplifying in decimals, we get
\(0.25+0.025+0.0025+0.00025=0.27775
eq0.4444\)
b) \(\frac{1}{40}+\frac{1}{400}+\frac{1}{4,000}+\frac{1}{40,000}\)
on simplifying in decimals, we get
\(0.025+0.0025+0.00025+0.000025=0.027775
eq0.4444\)
c)\(\frac{4}{10}+\frac{4}{100}+\frac{4}{1,000}+\frac{4}{10,000}\)
on simplifying in decimals, we get
\(0.4+0.04+0.004+0.0004=0.4444\)
Thus, this geometric series represent 0.4444.
d)\(\frac{1}{10}+\frac{1}{100}+\frac{1}{1,000}+\frac{1}{10,000}\)
on simplifying in decimals, we get
\(0.1+0.01+0.001+0.0001=0.1111\
eq0.4444\)
