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Series 12
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The program is written here to calculate the value of the series 1/2 - 2/3 + 3/4 - 4/5 + 5/6 - ...... n. The number of terms is taken as input from the user. A for loop is used here to find the value of the series.
If the value of ‘n’ is 3 then the value of the series will be:
1/2-2/3+3/4=0.58333333333333 (approx..)
Algorithm
INPUT: Number of terms
OUTPUT: Value of the series
PROCESS:
Step 1: [Taking the input]
Read n [number of terms]
Step 2: [Calculating the value of the series]
Set s<-0
Set sign<-1
[Calculating the series]
For i=1 to n repeat
Set s<-s+(sign×(i/(i+1)))
Set sign<-sign×(-1)
[End of ‘for’ loop]
[Printing the result]
Print "The value of the series is: s"
Step 3: Stop.
Code
TIME COMPLEXITY:
for(i=1;i<=n;i++)-----------------------------O(n)
{
s=s+(sign*(i/(i+1)));
sign=sign*(-1);
}
The time complexity of this program is O(n) where ‘n’ is the number of terms of the series
SPACE COMPLEXITY:
The space complexity of this program is O(1) as it requires a constant number of memory spaces for any given input.
