Question

Test the series. Of 1 − 1/2 + 1/4 − 1 /8 + 1/16 − · · · .

Answer 1

Answer:

1/32+1/64-1/128

Step-by-step explanation:

the denominator is doubled and one time add and other time subtraction.

Answer 2

The above series is in GP(Geometric progression) with the first term as 1 and the common ratio as (-1/2) and the Sum is equal to (2/3).

• We check whether the given sequence is in AP or GP.
• For as series to be in AP we need to find the difference between consecutive terms and check whether the common difference is same.
• If the common difference is same between consecutive terms then the series is said to be in AP.
• But here the common difference between terms is not same so the series is not in AP.
• Now we check if the series in is GP or not.
• Now  we calculate the common ratio between consecutive terms and check the ratio.
• We get the same ratio between the consecutive terms  that is (-1/2)
• Now we apply the formula for sum of infinite GP, which is equal to $\frac{a}{1-r}$.
• Sum = $\frac{1}{1 - (-1/2)}$

Sum = $\frac{1}{1 + 1/2}$

Sum = $\frac{2}{3}$