Question

Find the sum of series upto n terms:
8+88+888+.....................

Answer 1

8 ( 1,11,111,...............). And divide and multiple 9

Answer 2

8 + 88 + 888 + 8888 +........up to n times
= 8(1) + 8(11) + 8(111) + 8(1111) +........up to n times
= 8{ 1 + 11 + 111 + 1111 + ....... up to n times}
= 8/9{9 + 99 + 999 + 9999 + ..... up to n times}
= 8/9 { (10-1 )+ (100-1) + (1000-1) + (10000-1) + ........up to n times}
= 8/9 { (10 + 100 + 1000 + 10000 +...... n times) - (n×1)}
= 8/9{ ( (10×(10^n -1))/(10-1) ) -n }