Mathematical induction

waistyle

已知的1x2+2x3+3x4+....+n(n+1)=1」3n(n+1)(n+2)

問題:Hence or otherwise find the values of the following expressions
1+(1+2)+(1+2+3)+...+(1+2+3+....100)

Naozumi

用sum of arithmetic sequence
1 = 1(1+1)/2 = 1(2)/2
1+2 = 2(1+2)/2 = 2(3)/2
1+2+3 = 3(1+3)/2 = 3(4)/2
...
1+2+3+...+100 = 100(1+100)/2 = 100(101)/2

1+(1+2)+(1+2+3)+...+(1+2+3+....100)
= 1(2)/2 + 2(3)/2 + 3(4)/2 + ... + 100(101)/2
= [1(2) + 2(3) + 3(4) + ... +100(101)]/2