Question 1189130
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(1) Show that the formula is true for n=1<br>
For n=1, the formula says<br>
{{{1 = (1(3(1)-1)/2)}}}
{{{1 = 2/2}}}
{{{1 = 1}}} TRUE<br>
(2) Show that, if the formula is true for some n, it is also true for n+1<br>
We assume, as the formula says, that 1+4+7+...+(3n-2) is equal to {{{(n(3n-1))/2}}} and add the next term ({{{3(n+1)-2}}}, or {{{3n+1}}}) and show that the resulting expression is equal to {{{((n+1)(3n+2))/2}}}<br>
{{{(n(3n-1))/2+3n+1}}}
={{{(3n^2-n)/2+(6n+2)/2}}}
={{{(3n^2+5n+2)/2}}}
={{{((n+1)(3n+2))/2}}}<br>
The proof by induction is complete.<br>