# A solution to Signals and Systems (2nd Edition Oppenheim) – 1.54(c)

1.54 The relations considered in this problem are used on many occasions throughout the book

(c)show also if,then

**Method one**– dislocation subtraction

let

and

then we make a subtraction

let and we will get:

in it,,which means that this part can be eliminated,then we will make a summation for the rest of the part,which is a form of geometric progression.

**Method two**

Note that if we expand this complex summation formula and combine some parts,perhaps it will be a little easy.

There are two parts,in which,,as a result

- Method three,as the manual solution to this book gives:

Note that

then differentiating both sides of it,we get

finally