Question

观察下列等式2^4=7+9,3^4=25+27+29,4^4=61+63+65+67,5^4=121+123+125+1

Answer 1

2^4=7+9=2^3-1 +2^3+1=2X2^3=2^4

3^4=3^3-2+3^3+3^3+2=3X3^3=3^4

11^4=11^3-10+11^3-8+11^3-6+11^3-4+11^3-2+11^3+11^3+2+11^3+4+11^3+6+11^3+8+11^3+10=11X11^3=11^4

n^4裂成等差数列的和,项数=n,n为偶数时,公差为1.n为奇数时公差2.

首项=n^3 -n+1