Summation homework problem

In summary, the given equation can be simplified to (2^n-1)*lg 2 + lg(n+1). The mistake in the attempt was corrected by using the formula for the sum of consecutive integers and simplifying the expression. The final answer is correct.
  • #1
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Homework Statement



[tex]\sum^{n}_{r=1}(\lg \frac{2^r(r+1)}{r})=\sum^{n}_{r=1}[\lg 2^r+\lg (r+1)-\lg r][/tex]

Homework Equations





The Attempt at a Solution



i found the answer to be [tex](2^n-1)\lg 2 +\lg (n+1)[/tex]

Am i correct , or it can be further simplified ? Thanks .
 
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  • #2
Hi thereddevils! :smile:

Your lg(n+1) is fine, but the two-y part isn't …

how did you manage to get a 2n outside the lg ? :wink:
 
  • #3


tiny-tim said:
Hi thereddevils! :smile:

Your lg(n+1) is fine, but the two-y part isn't …

how did you manage to get a 2n outside the lg ? :wink:

Thanks , tiny tim !

oh , \sum^{n}_{r=1}\lg 2^r=\lg 2+2\lg 2+3\lg 2 +...

=\lg 2 (1+2+3+...)

=\frac{n}{2}(n+1)\lg 2

i think i see my mistake , is this correct ?
 
  • #4
(have a sigma: ∑ and try using the X2 tag just above the Reply box :wink:)

Yes, that's all correct now! :smile:
 

1. What is summation?

Summation is a mathematical process of adding together a sequence of numbers. It is represented by the symbol ∑ and can also be referred to as the sum or total.

2. What is a summation homework problem?

A summation homework problem is a mathematical question that requires the use of the summation process to find the answer. It usually involves adding together a sequence of numbers or terms using the ∑ symbol.

3. How do I solve a summation homework problem?

To solve a summation homework problem, you need to first determine the sequence of numbers or terms that need to be added together. Then, use the ∑ symbol and write out the expression. Finally, substitute the values of the sequence into the expression and solve for the answer.

4. What are some common formulas used in summation problems?

Some common formulas used in summation problems include arithmetic series, geometric series, and binomial series. These formulas can help simplify the process of finding the sum of a sequence of numbers or terms.

5. How can I check if my answer to a summation homework problem is correct?

You can check your answer to a summation homework problem by using a calculator or by manually calculating the sum. Additionally, you can use online tools or ask a teacher or classmate to verify your answer.

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