math 通項

A)let T(n) be the nth term
T(n)=T(n-1)+n+1
T(n-1)=T(n-2)+(n-1)+1
T(n-2)=T(n-3)+(n-2)+1
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T(2)=T(1)+2+1
+ T(1)=3
T(n)+T(n-1)+T(n-2)+...+T(2)+T(1) =T(n-1)+T(n-2)+T(n-3)+...+T(1) +3
+(n-1)(n+2)/2+(n-1)+3
T(n)=(n+2)(n+1)/2
B) T(n)=T(n-1)+2(n-1)
T(n-1)=T(n-2)+2(n-2)
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T(2)=T(1)+2(1)
+ T(1)=1
T(n)+T(n-1)+...+T(2)+T(1) = T(n-1)+...+T(2)+T(1) +(n-1)(n)+1
T(n)=n^2-n+1

C) T(n)=T(n-1)+2n
T(n-1)=T(n-2)+2(n-1)
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T(2)=T(1)+2(2)
+ T(1)=1
T(n)+T(n-1)T(n-2)+...T(2)+T(1) =T(n-1)T(n-2)+...T(2)+T(1) +(n-1)(n+2)+1
T(n)=n^2+n-1