Question

3+3/5+3/25+3/125+3/625

Answer 1

A = 3+ 3/5+ 3/25+ 3/125+ 3/625

A = 3/1+ 3/5+ 3/25+ 3/125+ 3/625

A = 1875/625 + 375/625 + 75/625 + 15/625 + 3/625

A = 3 + 0,6 + 0,12 + 0,024 + 0,0048

A = 3,6 + 0,12 + 0,024 + 0,0048

A = 3,72 + 0,024 + 0,0048

A = 3,744 + 0,0048

A = 3,7488

Answer 2

       A =     3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) + \(\dfrac{3}{625}\)

5\(\times\)A =   15 +  3 +   \(\dfrac{3}{5}\)  +  \(\dfrac{3}{25}\)  + \(\dfrac{3}{125}\)

5 \(\times\) A - A = 15 + 3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) - (3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) + \(\dfrac{3}{625}\))

4 \(\times\) A     = 15 + 3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) - 3   - \(\dfrac{3}{5}\) - \(\dfrac{3}{25}\) - \(\dfrac{3}{125}\) - \(\dfrac{3}{165}\)

4  \(\times\) A =  (15 - \(\dfrac{3}{625}\)) + (3 - 3) + (\(\dfrac{3}{5}\) - \(\dfrac{3}{5}\)) + (\(\dfrac{3}{25}-\dfrac{3}{25}\)) + (\(\dfrac{3}{125}\)-\(\dfrac{3}{125}\))

4 \(\times\) A =   \(\dfrac{9372}{625}\)

       A = \(\dfrac{9372}{625}\) : 4

       A = \(\dfrac{2343}{625}\)