sum of the first 20 termsof the sequence

0.7+0.07+0.007+..................... is

The whole of initial 20 terms can be found by 0.7+0.07+0.007 +… 20terms. Taking 7 regular we get 7(0.1+0.01+0.001+… . 20 terms) we have n = 20, a = 0.1 and r = 0.1 and utilizing recipe for geometric arrangement we get 0.7777. Which is the total of initial 20 terms.