數學歸納法證明4題1.1‧2^2 +2‧3^2+3‧4^2+......+n(n+1)^2= n(n+1)(n+2)(3n+5)/12【證明】:-----------------------------------------------------------------------------2.1/1+1/(1+2)+......1/(1+2+.....+n)=2n/(n+1)【證明】:-------------------------------------------------------------------------3.n^3+(n+1)^3+(n+2)^3是9的倍數【證明】: ----------------------------------------------------------------------------4.對於任意大於或等於3的正整數n，5^n>3^n+4^n成立。【證明】:原連結 1.1‧2^2 +2‧3^2+3‧4^2+......+n(n+1)^2= n(n+1)(n+2)(3n+5)/12【證明】:1)n=1時, 左式=1(2)^2=4, 右式=1‧2‧3‧8/12=4, ∴原式成立2)假設n=k時, 命題成立即1‧2^2...
