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**booper563** Jacques noticed that they added an even number of blockes in each step. They started with 2, then added 4, and then added 6. He also noticed that the total number of blocks was related to the number of adjacent towers.

Number of towers. total number of blocks

1 2=1*2

2 2+4=6 =2*3

3 2+4+6=12 =3*4

Jacques concluded that the sum of the first n even numbers is n(n+1); that is,

2+4+6+...+2n=n(n+1)

a.)Jacques mother observed that 2+4+5+...+2n is an example of an arithmetic series and that the sum of the terms of an arithmetic series is determined as follows:

t1+t2+t3+...tn = n(t1+tn)/2

Prove Jacques conjecure using this formula. Is the proof an example of inductive reasoning or deductive reasoning? Explain.