find the value of 5+55+55+555+…………..+ n

Solution

5+55+55+555+…………..+ n terms 5(1+11+111+………………………+ n terms) Multiply and divide by 9 9/9 × 5(1+11+111+………………………+ n terms) 5/9 × (9+99+999+ …………………+ n terms) 5/9 × [(10-1) + (100-1) + (1000-1) +…………… + n terms] 5/9 × [(10 + 10² + 10³ +………+ n terms) – (1+1+1+………+ n terms)] 5/9 × [(10 + 10² + 10³ +………+ n terms) – n] In the series [10 + 10² + 10³ +………+ n terms] First term, a = 10              common ratio, r = 10 Sum of n terms = (a(r^n-1))/((r-1)) Therefore The required answer = 5/9 [((10(〖10〗^n-1))/9 - n)]