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采用直接推导法求解下列递归方程 T(1)=1 T(n)=T(n-1)+n 当n>1
递归方程:
[egin{cases} T(1)=1 \ T(n)=T(n-1)+n &(n>1)& end{cases} ]
直接推导法求解:
[egin{align} T(n)&=T(n-1)+n&\ &=T(n-2)+n+n-1&\ &=T(n-3)+n+n-1+n-2&\ cdots\ &=n+n-1+n-2+n-3+cdots+2+1& \\ Rightarrow &T(n)=frac{n*(n+1)}{2}& end{align} ]
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