Find the sum of the following series :
0.5 + 0.55 + 0.555 + …. to n terms
Let
S = 0.5 + 0.55 + 0.555 + .....n terms
Taking 5 as common we get,
S = 5(0.1 + 0.11 + 0.111 + ...nterms)
Multiply and divide by 9
⇒ )
⇒ )
⇒
⇒
Now 1 + 1 + 1 + ..n = n
For 0.1 + 0.01 + 0.001 + ..nterms
∴ Common Ratio = r =
∴ Sum of GP for n terms = …(1)
⇒ a = 0.1, r = , n = n
∴ Substituting the above values in (1) we get
⇒
⇒
For second term the summation is n.
∴
⇒