I'm stuck on this summation problem $$\sum_{k=0}^4 (-1)^k\sum_{l=k+1}^5l$$

I can solve both of the summations, but I don't know what to do when they're next to each other like that, the answer should be $$9$$ and I have no idea how to get to that. Any help would be much appreciated, thank you very much

closed as off-topic by Henrik, Mark, Namaste, Don Thousand, ArsenBerkOct 19 '18 at 22:09

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, Mark, Namaste, Don Thousand, ArsenBerk
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• As $k$ (the variable the first sum is over) is used in the second sum, it's an inner sum (i.e. there could - some would say should, for clarity - have been parentheses around $(-1)^k$ and the second sum). As you say you can do that sum, do so, then you'll have one sum left. – Henrik Oct 19 '18 at 19:14
• Thank you very much, I think I overestimated myself (with knowing how to do it) because even so, I still can't get to the number 9. I think it would help me to see the steps, because I'm starting to feel hopeless – G.Jan Oct 19 '18 at 19:46

The second sum is part of the first sum. For each $$k$$ from $$0$$ to $$4$$, you are meant to evaluate $$(-1)^k\sum_{l=k+1}^5 l$$. Then you take those five results and add them.
• @G.Jan $(-1)^k\sum_{l=k+1}^5 l$ for $k=0$ becomes $(-1)^0\sum_{l=1}^5 l=1\cdot(1+2+3+4+5)=15$. Then for $k=1$ we get ... – Arthur Oct 19 '18 at 20:35