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Try this! The sum of first 20 terms of the sequence 0.7 ,0.77,0.777,.........,is :

The sum of first 20 terms of the sequence 0.7 ,0.77,0.777,.........,is :

  • Option 1)

    \frac{7}{9}\left ( 99+10^{-20} \right )

  • Option 2)

    \frac{7}{81}\left ( 179-10^{-20} \right )

  • Option 3)

    \frac{7}{9}\left ( 99-10^{-20} \right )

  • Option 4)

    \frac{7}{81}\left ( 179+10^{-20} \right )

 
Answers (2)
282 Views
N neha

As we learnt

 

Sum of infinite terms of a GP -

a+ar+ar^{2}+- - - - -= \frac{a}{1-r}\\here \left | r \right |<1

- wherein

a\rightarrow first term

r\rightarrow common ratio

 

 S=0.7+0.77+0.777...upto\: \: 20\: \: terms

S=\frac{7}{9}(0.9+0.99+0.999...)

S=\frac{7}{9}(1-0.1+1-0.01+1-0.001...)

S=\frac{7}{9}(20-(\frac{1}{10}+\frac{1}{100}+...upto\: \: 20\: \: terms))

S=\frac{7}{9}(20-\frac{\frac{1}{10}(1-\frac{1}{10^{20}})}{(1-\frac{1}{10})})

S=\frac{7}{9}(20-\frac{1-10^{-20}}{9})

S=\frac{7}{81}(179+10^{-20})

 


Option 1)

\frac{7}{9}\left ( 99+10^{-20} \right )

Option 2)

\frac{7}{81}\left ( 179-10^{-20} \right )

Option 3)

\frac{7}{9}\left ( 99-10^{-20} \right )

Option 4)

\frac{7}{81}\left ( 179+10^{-20} \right )

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