Sum of n terms of the series 0 1+ 0 11 + 0 111 + is - Quantitative Aptitude - Sequence and Series - Arithmetic and Geometric Progressions

Question

Sum of n terms of the series 0 1+ 0 11 + 0 111 +
is

Manbar Singh · Accepted Answer

0 1 + 0 11 + 0
111 +  +n terms=190 9 + 0 99 + 0
999 + 
+ n terms=191 - 110 + 1 - 1100 + 1 - 11000 + 
+ n terms=191 - 110 + 1 - 1102 + 1 - 1103 + 
+1 - 110n =19n - 110 + 1102 + 1103 + 
 + 110n=19n - 110×1 - 1/10n1 - 1/10=19n - 191 - 110n=1819n - 1 + 110n

Sum of n terms of the series 0.1+ 0.11 + 0.111 + ... is