Question

What is the sum of the series?

∑k=36(−2k+5)



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Answer 1

Hello !

Answer:

`\large \boxed{\sf \sum\limits^6_(k=3)(-2k+5)=-16}`

Explanation:

We want to calculate the following sum :

`\sf \sum\limits^6_(k=3)(-2k+5)`

Let's remember the following property :

`\fbox{\begin{tabular}{1\textwidth}\star\ \underline{\sf Linearity:}\\ \sf \sum\limits^n_(k=n_0)(\alpha a_k+\beta b_k)=\alpha\sum\limits^n_(k=n_0) a_k+\beta \sum \limits^n_(k=n_0)b_k\end{tabular}}`

Now we can apply this property to our formula :

`\sf \sum\limits^6_(k=3)(-2k+5)\\=-2\sf \sum\limits^6_(k=3)(k)+\sum\limits^6_(k=3)5`

Now we can calculate :

`\sf \sum\limits^6_(k=3)(-2k+5)\\=-2(3+4+5+6)+(6-3+1)5\\=-2*18+4* 5\\=-36+20\\\boxed{\sf \sum\limits^6_(k=3)(-2k+5)=-16}`

Have a nice day ;)