- #1

smart_worker

- 131

- 1

## Homework Statement

find the general formula to calculate the sum

## Homework Equations

1+11+111+1111+11111+....upto n terms

## The Attempt at a Solution

10

^{0}+ (10

^{1}+10

^{0}) + (10

^{2}+10

^{1}+ 10

^{0}) + (10

^{3}+ 10

^{2}+10

^{1}+ 10

^{0}) + ...

==> (10

^{0}+10

^{0}+10

^{0}+...upto n terms) + (10

^{1}+10

^{1}+10

^{1}+...upto n-1 terms) + (10

^{2}+10

^{2}+10

^{2}+...upto n-2 terms) + ..........+ (10

^{n-2}+ 10

^{n-2}) + (10

^{n-1})

==>n + (10

^{1}+10

^{1}+10

^{1}+...upto n-1 terms) + (10

^{2}+10

^{2}+10

^{2}+...upto n-2 terms) + ......+ (10

^{n-2}+ 10

^{n-2}) + (10

^{n-1})

after this i don't know how.They seem to resemble geometric series.