- #1
mateomy
- 307
- 0
The problem posed is:
Evaluate
[tex]
\sum_{i=1}^{n} (2i + 2^i)
[/tex]
I know that I can break the summation down to this:
[tex]
2\sum_{i=1}^{n} i\, +\, 2\sum_{i=1}^{n}1^i
[/tex]
and then after using some Fundamental Theorems...
[tex]
=2\Bigg(\frac{n(n+1)}{2}\Bigg) + 2^n
[/tex]
I can't seem to get it to look like my answer key which is...
[tex]
2^{n+1} + n^2 + n-2
[/tex]
Clearly I am doing something wrong, I know I can expand my last step but when I do, it doesn't look anything close to what the book is showing me. Particularly, where are they getting the n-2 ? Where is my step wrong? THanks in advance for any help.
Evaluate
[tex]
\sum_{i=1}^{n} (2i + 2^i)
[/tex]
I know that I can break the summation down to this:
[tex]
2\sum_{i=1}^{n} i\, +\, 2\sum_{i=1}^{n}1^i
[/tex]
and then after using some Fundamental Theorems...
[tex]
=2\Bigg(\frac{n(n+1)}{2}\Bigg) + 2^n
[/tex]
I can't seem to get it to look like my answer key which is...
[tex]
2^{n+1} + n^2 + n-2
[/tex]
Clearly I am doing something wrong, I know I can expand my last step but when I do, it doesn't look anything close to what the book is showing me. Particularly, where are they getting the n-2 ? Where is my step wrong? THanks in advance for any help.
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