Question

Please Explain in detail and show all working

Answer 1

did you try to find the error

Answer 2

| sqrt(2)-17/12| =0.002453105
|sqrt(2)-41/29| = 0.000420459
|sqrt(2)-99/70| =0.000072152
|sqrt(2)- 239/169 |= 0.000012379
|sqrt(2)- 577/408 |=0.000002124

If you divide successive errors, you should get the factor that the error reduces by.
For instance
0.000420459 / 0.002453105 =0.1714
0.000072152 / 0.000420459=0.1716
0.000012379 / 0.000420459= 0.1716
0.000002124 / 0.000012379= 0.1716
to 4 decimal places

Answer 3

kk got it thanks @perl