II: An Interesting Problem zt We have seen that the p-series seen the value to w
ID: 3605812 • Letter: I
Question
II: An Interesting Problem zt We have seen that the p-series seen the value to which it con Do 2R2 converges by the integral test, but we have not verges. We can approximate this value by looking at the terms in the sequence of partial sums Problem 4: Suppose ak and let Using Excel, or a program of your choice, calculate the given terms below to 6 decimal termas below to s decimal places. To check your work, make sure your answer to s100 agr ees with the given one. S5 = 810 $50 = 1.634984 S 100 8500 81000 = One of the earliest "derivations" of the exact value of this series was given by Leonard Euler in 1734 by using Taylor series. The following will walk you through his argument.Explanation / Answer
Here is the C program to calculate the above formula.
/************************/
#include <stdio.h>
#include <math.h>
int main()
{
printf("Enter n ");
int n;
scanf("%d",&n);
int i;
double sum=0.0;
for(i=1;i<=n;i++)
{
sum=sum+ (1/pow(i,2));
}
printf("Sum: %f ",sum);
return 0;
}
/*************************/ Here is the output
kuhu@kuhu-X540LA:~/tanmay/chegg$ ./a.out
Enter n 1
Sum: 1.000000
kuhu@kuhu-X540LA:~/tanmay/chegg$ ./a.out
Enter n 5
Sum: 1.463611
kuhu@kuhu-X540LA:~/tanmay/chegg$ ./a.out
Enter n 10
Sum: 1.549768
kuhu@kuhu-X540LA:~/tanmay/chegg$ ./a.out
Enter n 50
Sum: 1.625133
kuhu@kuhu-X540LA:~/tanmay/chegg$ ./a.out
Enter n 100
Sum: 1.634984
kuhu@kuhu-X540LA:~/tanmay/chegg$ ./a.out
Enter n 500
Sum: 1.642936
kuhu@kuhu-X540LA:~/tanmay/chegg$ ./a.out
Enter n 1000
Sum: 1.643935