=2[( 1/2- 1/3)+( 1/3- 1/4)+( 1/4- 1/5)+...( 1/50- 1/5 1)]

=2[ 1/2- 1/3+ 1/3- 1/4+ 1/4- 1/5+...+ 1/50- 1/5 1]

=2*( 1/2- 1/5 1)= 1-2/5 1=49/5 1

2.( 1) Equation 1: (1-3/5) A storage grain = (1-2/5) B storage grain.

Equation 2:A storage grain +B storage grain =450 tons.

It is found that the raw grain storage capacity of warehouse A is 270 tons, and that of warehouse B is 180 tons.

(2) The quantity of grain transported from warehouse A to warehouse C is X tons.

Total freight m=a*X+b*(200-X)=200*b+X(a-b)

The first case:

When a=0 or b=0 (the question doesn't mean that one of A and B can't be 0, in case it is an acquaintance's transportation company. . . )

Freight m=0 yuan;

The second case:

When A is greater than B, all the grain will be shipped out of warehouse B, that is, X=0 ton freight is the least, at this time, m=200b.

The third situation:

When A is less than B, all the grain is transported out of warehouse A, that is, X=200 tons, and the freight is the least. At this time, M = 200a.

The fourth situation:

When a=b, the freight is the same at this time, and the freight is m=200a=200b.