- #1

martina1075

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- 0

Member warned that some effort must be shown

- Homework Statement:
- Good afternoon 😃 Can someone explain to me how to change the bounds of summation using this example please?

- Relevant Equations:
- As per picture

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- Thread starter martina1075
- Start date

- #1

martina1075

- 7

- 0

Member warned that some effort must be shown

- Homework Statement:
- Good afternoon 😃 Can someone explain to me how to change the bounds of summation using this example please?

- Relevant Equations:
- As per picture

- #2

- 17,832

- 19,101

What does ##\sum_{i=k}^m a_i## stand for?

- #3

- 24,068

- 15,768

Try ##j = i - m + p##.

- #4

martina1075

- 7

- 0

i stands for the positive integer , ai stands for a unique number and m and n are positive integers with m being greater or equal to n.What does ##\sum_{i=k}^m a_i## stand for?

- #5

- 17,832

- 19,101

No, that's what the "numbers" mean. But what is the abbreviation ##\sum## for?i stands for the positive integer , ai stands for a unique number and m and n are positive integers with m being greater or equal to n.

- #6

- #7

SammyS

Staff Emeritus

Science Advisor

Homework Helper

Gold Member

- 11,745

- 1,330

(Notice that fresh has changed some of the variables from those in the problem statement.)i stands for the positive integer , aWhat does ##\sum_{i=k}^m a_i## stand for?_{i}stands for a unique number and m and n are positive integers with m being greater or equal to n.

Think of what @fresh_42 was getting at more like:

##\displaystyle \sum_{i=m}^n a_i## stands for:

##a_{m} + a_{m+1} + a_{m+2} + ... + a_{n-1} + a_{n} ##

In words, sum the ##a_i ## values, where ##i## takes on values from ##m## through ##n##.

With this in mind, do a similar translation for the right hand side. It may help to use an index other than ##i##, initially.

##\displaystyle \sum_{j=p}^{p+n-m} a_{j+m-p}##

Plug ##p## in for ##j## to get the index for the first term in the sum, then plug ##p+n-m## in for ##j## to get the index for the final term.

(Added in

Last edited:

- #8

archaic

- 688

- 210

You forgot to change ##i## to ##j## in the second symbol :)(Notice that fresh has changed some of the variables from those in the problem statement.)

Think of what @fresh_42 was getting at more like:

##\displaystyle \sum_{i=m}^n a_i## stands for:

##a_{m} + a_{m+1} + a_{m+2} + ... + a_{n-1} + a_{n} ##

In words, sum the ##a_i ## values, where ##i## takes on values from ##m## through ##n##.

With this in mind, do a similar translation for the right hand side. It may help to use an index other than ##i##, initially.

##\displaystyle \sum_{i=p}^{p+n-m} a_{j+m-p}##

Plug ##p## in for ##j## to get the index for the first term in the sum, then plug ##p+n-m## in for ##j## to get the index for the final term.

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