Find the sum of the geometric series 1+1/2+1/4+1/8+...to 12th terms,
sir how are this question answer 4095/2048
a = 1
r = 1/2
S12 = (1 - 1/2^12)/(1 - 1/2)
Well, this question is as tricky as trying to balance a clown on a unicycle. But fear not, for Clown Bot is here to help!
To find the sum of a geometric series, we can use the formula:
S = a * (1 - r^n) / (1 - r)
Where:
S = the sum of the series
a = the first term
r = the common ratio
n = the number of terms
In this case, the first term (a) is 1, the common ratio (r) is 1/2, and the number of terms (n) is 12. Plugging these values into the formula, we get:
S = 1 * (1 - (1/2)^12) / (1 - 1/2)
Simplifying further, we have:
S = 1 * (1 - 1/4096) / (1/2)
S = 2 * (4096 - 1) / 4096
S = 2 * 4095 / 4096
And finally:
S = 8190 / 4096
So, the sum of the geometric series is 8190/4096, or simplified as 4095/2048.
See, math can be just as fun as clowning around sometimes!
To find the sum of a geometric series, you can use the formula:
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 given series, the first term (a) is 1, and the common ratio (r) is 1/2. We want to find the sum of the first 12 terms.
Substituting these values into the formula:
S = 1(1 - (1/2)^12) / (1 - 1/2)
Simplifying:
S = (1 - 1/4096) / (1/2)
S = (4096/4096 - 1/4096) / (1/2)
S = (4095/4096) / (1/2)
S = (4095/4096) * (2/1)
S = (4095 * 2) / 4096
S = 8190 / 4096
S = 4095/2048
Therefore, the sum of the geometric series 1 + 1/2 + 1/4 + 1/8 + ... to the 12th term is 4095/2048.