Question

sum of the series 3+33+333+_to n terms

Answer 1

Answer:

S = 1/27 (10 (10ⁿ−1) − 9n)

Step-by-step explanation:

S = 3 + 33 + 333 + ....

S = 3 (1 + 11 + 111 + ....)

S = 3 [(1) + (1+10) + (1+10+100) + ... + (1+10+100+...+10^(n−1))

S = 3 [(10¹−1)/(10−1) + (10²−1)/(10−1) + (10³−1)/(10−1) + ... + (10ⁿ−1)/(10−1)]

S = 3/9 [(10¹ + 10² + 10³ + ... + 10ⁿ) − n]

S = 1/3 [10 (10ⁿ−1)/(10−1) − n]

S = 1/3 [10 (10ⁿ−1)/9 − 9n/9]

S = 1/27 (10 (10ⁿ−1) − 9n)

Answer 2

Answer:    1/27 [10(10^n -1)/9 - 9n/9]

Step-by-step explanation: