The sum of first 20 terms of the sequence0.7,0.77,0.777,..., is
781179-10-20
7999-10-20
781179+10-20
7999+10-20
Explanation for correct option:
Let ,
Sn=0.7+0.77+0.777+.....+0.777777...(20times)⇒Sn=70.1+0.11+0.111+.....+0.111111(20times)⇒Sn=790.9+0.99+0.999+...+0.9999999(20times)⇒Sn=791-0.1+1-0.01+1-0.001+....+1-0.000..01⇒Sn=7920-110+1102+1103+...+11020
We know that, the sum of the G.P=a1-rn1-r
⇒Sn=7920-1101-110201-110⇒Sn=7920-1-110209⇒Sn=7920-191-10-20⇒Sn=781179+10-20
Hence, option C is correct.
The sum of the first 20 term of the sqeuence 0.7, 0.77, 0.777,...., is (IIT JEE Main 2013)