Question

Find the sum to n terms $(7+77+777+.....n$ terms)

Answer 1

Let s be the sum of n terms of sumes,

(7+77+777+....n terms)

$\therefore$ 7+77+777+....n terms

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

$=\frac{7}{9}(9+99+999+....nterms)$

$=\frac{7}{9}\left[\right(10-1)+({10}^2-1\left)\right({10}^3-1)+....nterms]$

$=\frac{7}{9}\left[\right(10+{10}^2+{10}^3....tontrems\left)\right(1+1+...nterms\left)\right]$

$=\frac{7}{9}[\frac{10({10}^n-1)}{10-1}-n]$

$=\frac{7}{9}\left[\frac{10}{9}\right({10}^n-1)-n]$