Find the sum of the following series :
5 + 55 + 555 + … to n terms.
Taking 5 in common we get
5(1 + 11 + 111 + ....n)
Now Multiply and Divide by 9 we get
⇒ )
⇒ )
⇒
⇒
Now First term is in GP.
10, 100, 1000…to n terms
∴ Common Ratio = r =
∴ Sum of GP for n terms = …(1)
⇒ a = 10, r = 10, n = n
∴ Substituting the above values in (1) we get
⇒
⇒
For the second term the summation is n.
∴
⇒ .