Find the sum of the following series :
0.6 + 0.66 + 0.666 + …. to n terms.
Let
S = 0.6 + 0.66 + 0.666 + .....n terms
Taking 6 as common we get
S = 6(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.
∴
⇒