Find the sum of the series 0.5+0.55+0.555+....to n terms.
To find the sum of the series 0.5+0.55+0.555+....to n terms, we need to identify the pattern in the series and then use the formula to find the sum.
The given series is an arithmetic series because there is a constant difference between consecutive terms. We can see that the common difference is 0.05.
To find the nth term of the series, we can use the formula for the nth term of an arithmetic series:
nth term = a + (n-1)d
In this case, the first term (a) is 0.5 and the common difference (d) is 0.05. So the general formula for the nth term of the series is:
nth term = 0.5 + (n-1)(0.05)
Now, to find the sum of the first n terms of an arithmetic series, we use the formula for the sum of an arithmetic series:
sum = (n/2) * (2a + (n-1)d)
In this case, the first term (a) is 0.5, the common difference (d) is 0.05, and we want to find the sum of n terms.
Therefore, the formula for the sum of the series becomes:
sum = (n/2) * (2 * 0.5 + (n-1) * 0.05)
Simplifying this formula will give us the sum of the series in terms of n.