find the sum of the series 1-2/2+1/4+1/8.... to n terms.
I suspect a typo in the 2nd term.
Did you mean ...
1+1/2+1/4+1/8.... I will suspect as much
then a = 1 , r = 1/2
sum of n terms
= 1(1 - (1/2)^n )/(1 - 1/2)
= 2(1 - (1/2)^n )
= 2 - (1/2)^(n-1) or 2 - 2^(1-n)
testing my answer:
sum of first 4 terms, n = 4
= 1 + 1/2 + 1/4 + 1/8 = 15/8
using my answer:
sum = 2 - 2^-3
= 2 - 1/8 = 15/8
sir this question answer (2/3(1-(-1)^n/2^n)
To find the sum of the given series, we need to determine the pattern and use the formula for the sum of a geometric series.
Looking at the series: 1 - 2/2 + 1/4 + 1/8 + ...
We observe that the series is a geometric progression with a first term of 1 and a common ratio of -1/2. Each subsequent term is obtained by multiplying the previous term by -1/2.
The formula for the sum of a geometric series is:
S = a * (1 - r^n) / (1 - r)
Where:
S is the sum of the series
a is the first term
r is the common ratio
n is the number of terms in the series
In our case:
a = 1 (first term)
r = -1/2 (common ratio)
Now, we substitute these values in the formula and simplify it:
S = 1 * (1 - (-1/2)^n) / (1 - (-1/2))
= 1 * (1 - 1/2^n) / (1 + 1/2)
= 1 * (1 - 1/2^n) / (3/2)
= 2/3 * (1 - 1/2^n)
Therefore, the sum of the series 1 - 2/2 + 1/4 + 1/8 + ... to n terms is 2/3 * (1 - 1/2^n).