# The sum of first 20 terms of the sequence 0.7 ,0.77,0.777,.........,is : Option 1) Option 2) Option 3) Option 4)

N neha
H Himanshu

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)

Option 2)

Option 3)

Option 4)

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