计算:2^2/1*3+3^2/2*4+…+99^2/98*100

题目

计算:2^2/1*3+3^2/2*4+…+99^2/98*100
.不太详细也可以,只要看得懂...加油..悬赏看情况加..

答案

2^2/1*3+3^2/2*4+…+99^2/98*100
=2^2/1*3-1/1*3+1/1*3+3^2/2*4-1/2*4+1/2*4+…+99^2/98*100-1/98*100+1/98*100
=2^2/1*3-1/1*3+3^2/2*4-1/2*4+…+99^2/98*100-1/98*100+1/1*3+1/2*4+.+1/98*100
=(2^2-1)/1*3+(3^2-1)/2*4+…+(99^2-1)/98*100+(2/1*3+2/2*4+.+2/98*100)/2
=(2-1)(2+1)/1*3+(3-1)(3+1)/2*4+…+(99-1)(99+1)/98*100+(1-1/3+1/2-1/4+.+1/98-1/100)/2
=1*3/1*3+2*4/2*4+…+98*100/98*100+(1+1/2-1/99-1/100)/2
=1+1+.+1+(1-1/99+1/2-1/100)/2
=98+(98/99+49/100)/2
=98+49(2/99+1/100)/2
=98+49(200/9900+99/9900)/2
=98+49(299/9900)/2
=98+14651/19800
=98又14651/19800