Find the sum.
1 − 1/2+1/4-1/8+....-1/512
To find the sum of the given sequence 1 − 1/2 + 1/4 - 1/8 + .... - 1/512, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, the first term, a, is 1, and the common ratio, r, is -1/2.
So, plugging these values into the formula:
S = 1 / (1 - (-1/2)),
Simplifying further:
S = 1 / (1 + 1/2),
S = 1 / (3/2),
S = 2/3.
Therefore, the sum of the given sequence is 2/3.
did you recognize the series as a geometric series with
a = 1 and r = -1/2 ??
If you are studying this topic you MUST know the formula for the sum of n terms
hint: how many terms are there ?
look at this patters
term(2) = -1/2 = -1/2^1
term(3) = 1/4 = +1/2^2
term(4) = -1/8 = -1/2^3
...
term(n) = -1/2^9
mmmmhhhh?