Question

Evaluate .7 + .77 + .777 + ……, in terms of a rational number.

Answer 1

Hlo

Here is solution

7+77+777+7777........nterms

=7 (1+11+111+1111......n)

=7/9 (9+99+999+9999....n)

=7/9 ((10-1)+(10^2-1)+(10^3-1)+....n)

=7/9 ((10+10^2+10^3...n)-(1+1+1+1.....n))

=7/9 ((10 (10^n-1)/(10-1))-n)