Given: sequence: 8, 88, 888, 8888… .

S_n = 8 + 88 + 888 + 8888 + …….

⇒ S_n = 8[1 + 11+ 111 + 1111 +…….]

⇒ S_n = × [9 + 99+ 999 + 9999 +…….]

⇒ S_n = × [(10 – 1) + (10² – 1)+ (10³ – 1) + (10⁴ – 1) +…….]

⇒ S_n = × [10 + 10² + 10³ + 10⁴ +…….] – × [1 + 1+ 1 +1 +…….]

⇒ S_n = × [10 + 10² + 10³ + 10⁴ +…….] – × [1 + 1+ 1 +1 +…….]

⇒S_n = (∵ sum of n terms of G.P is , here a = 10 and r = 10)

⇒S_n =

⇒S_n =

⇒S_n =

∴