1/1*2*3+1/2*3*4+...+98*99*100= 5
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consider
1/[(n+1)(n+2)(n+3)]
=(1/2){ 1/[(n+1)(n+2)] - 1/[(n+2)(n+3)] }
1/(1*2*3)+1/(2*3*4)+...+1/(98*99*100)
=(1/2) { [1/(1*2)-1/(2*3)] +[1/(2*3) -1/(3*4)]+...+[1/(98*99)-1/(99*100)] }
=(1/2)[ 1/2 - 1/9900 ]
=4949/19800
1/[(n+1)(n+2)(n+3)]
=(1/2){ 1/[(n+1)(n+2)] - 1/[(n+2)(n+3)] }
1/(1*2*3)+1/(2*3*4)+...+1/(98*99*100)
=(1/2) { [1/(1*2)-1/(2*3)] +[1/(2*3) -1/(3*4)]+...+[1/(98*99)-1/(99*100)] }
=(1/2)[ 1/2 - 1/9900 ]
=4949/19800
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