Saved Bookmarks
| 1. |
7+77+777+............+777.......7=7/81(10n+1 - 9n -10) |
| Answer» Sn = 7 + 77 + 777 + ---- + n terms{tex}= \\frac { 7 } { 9 } [ 9 + 99 + 999 + - - - - + n \\text { terms } ]{/tex}{tex}= \\frac { 7 } { 9 }{/tex}[(10 - 1 ) + (102\xa0- 1) + (103\xa0- 1) + --- + n terms]{tex}= \\frac { 7 } { 9 }{/tex}[(101 + 102 + ---- +n terms) - (1 + 1 + 1 ---- + n terms)]{tex}= \\frac { 7 } { 9 } \\left[ \\frac { 10 \\left( 10 ^ { n } - 1 \\right) } { 10 - 1 } - n \\right]{/tex}{tex}= \\frac { 7 } { 9 } \\left[ \\frac { 10 \\left( 10 ^ { n } - 1 \\right) } { 9 } - n \\right]{/tex} | |