Answer:
Hence, the conjecture for the sum of first 20 positive integer is:
20×21=420
Step-by-step explanation:
The table is given as:
2 = 2 =1.2
2+4 = 6 = 2.3
2+4+6 = 12 = 3.4
2+4+6+8 = 20 = 4.5
2+4+6+8+10 = 30 = 5.6
Hence, we see the pattern as:
2+4+6+....+2n= n(n+1)
which is the sum of first n even positive integers.
Hence, we are asked to find the sum of first 20 positive even numbers that is we are asked to find the sum when n=20.
i.e. the sum of:
2+4+6+8+..........+40=20(20+1)
2+4+6+8+........+40=20×21=420.
Hence, the conjecture for the sum of first 20 positive integer is:
20×21=420
