Why is the following summation equal to the following formula? Could you guys show a proof?
$$\sum_{j=1}^{n} k = k*n$$
Proof why the following summation equals the following formula
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$\begingroup$
proof-verification
summation
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4Note $$\sum_{j=1}^{n}a_j=a_1+a_2+\cdots+a_n $$ Set $a_1=a_2=\cdots=a_n=k$ thus $$\sum_{j=1}^{n}k=\underbrace{k+k+\cdots+k}_{n}=kn$$ – 2017-01-06
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0The summand is constant with respect to $j$ so you are just summing the number $k$ to itself $n$ times. – 2017-01-06
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0Can you explain what $\sum_{j = 1}^n k$ means? If you can, you should be able to explain the "why" part. I would use induction for the actual proof (if, after explaining "why", such a thing needs proof). – 2017-01-06
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1@BehrouzMaleki thanks man! I suggest adding it as an answer though, because it completely answers my question! – 2017-01-06
1 Answers
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$$\sum_{j=1}^n k = \underbrace{k + k + \ldots + k}_n = k \times n.$$