Question

${} \{ = > find \: the \: sum \: to \: n \: terms \: of \\ \: the \: sequence \: 8 \: 88 \: 888 \: 8888..............$
${} \huge \red{ answer \: it.....}$
​

Answer 1

Answer:

ans is

8 10(10^n-1)

-----{ ------------------- - n}

9 9

Step-by-step explanation:

formula used

a(r^n-1)

1----->S =---------------

n (r-1)

2------->1+1+1+1+.......to n terms=n

now

S=8+88+888+...................

=8(1+11+111+...............)

8

= -----(9+99+999+...........)

9

8

= -------{(10-1)+(100-1)+(1000-1)+..........}

9

8

=---------{(10+100+1000+....)-(1+1+1+.....)}

9

8 10(10^n-1)

=---------{-------------------- - n }

9 (10-1)

8 10(10^n-1)

=---------{ -------------------- -n}

9 9

Answer 2

refer to the attachment