<Dl> <Dd> π = 3 + 4 2 × 3 × 4 − 4 4 × 5 × 6 + 4 6 × 7 × 8 − 4 8 × 9 × 10 + ⋯ (\ displaystyle \ pi = 3 + (\ frac (4) (2 \ times 3 \ times 4)) - (\ frac (4) (4 \ times 5 \ times 6)) + (\ frac (4) (6 \ times 7 \ times 8)) - (\ frac (4) (8 \ times 9 \ times 10)) + \ cdots) </Dd> </Dl> <Dd> π = 3 + 4 2 × 3 × 4 − 4 4 × 5 × 6 + 4 6 × 7 × 8 − 4 8 × 9 × 10 + ⋯ (\ displaystyle \ pi = 3 + (\ frac (4) (2 \ times 3 \ times 4)) - (\ frac (4) (4 \ times 5 \ times 6)) + (\ frac (4) (6 \ times 7 \ times 8)) - (\ frac (4) (8 \ times 9 \ times 10)) + \ cdots) </Dd> <P> The following table compares the convergence rates of these two series: </P> <Table> <Tr> <Th> Infinite series for π </Th> <Th> After 1st term </Th> <Th> After 2nd term </Th> <Th> After 3rd term </Th> <Th> After 4th term </Th> <Th> After 5th term </Th> <Th> Converges to: </Th> </Tr> <Tr> <Td> π = 4 1 − 4 3 + 4 5 − 4 7 + 4 9 − 4 11 + 4 13 ⋯ . (\ displaystyle \ pi = (\ frac (4) (1)) - (\ frac (4) (3)) + (\ frac (4) (5)) - (\ frac (4) (7)) + (\ frac (4) (9)) - (\ frac (4) (11)) + (\ frac (4) (13)) \ cdots .) </Td> <Td> 4.0000 </Td> <Td> 2.6666...</Td> <Td> 3.4666...</Td> <Td> 2.8952...</Td> <Td> 3.3396...</Td> <Td> π = 3.1415...</Td> </Tr> <Tr> <Td> π = 3 + 4 2 × 3 × 4 − 4 4 × 5 × 6 + 4 6 × 7 × 8 ⋯ . (\ displaystyle \ pi = (3) + (\ frac (4) (2 \ times 3 \ times 4)) - (\ frac (4) (4 \ times 5 \ times 6)) + (\ frac (4) (6 \ times 7 \ times 8)) \ cdots .) </Td> <Td> 3.0000 </Td> <Td> 3.1666...</Td> <Td> 3.1333...</Td> <Td> 3.1452...</Td> <Td> 3.1396...</Td> </Tr> </Table>

Application of pi in and outside the subject maths