Evaluate the summation $\sum\limits_{i=1}^n\sum\limits_{j=1}^i 4$

Asked Apr 14 '21 at 23:37

Active Apr 14 '21 at 23:50

Viewed 37 times

Can somebody explain to me step by step how you solve this problem.

Evaluate the summation $$\sum\limits_{i=1}^n\sum\limits_{j=1}^i 4$$

This is what I did:

1)I did the inner summation which gives us $4i$.

2)I did the outer summation which is $4(1)+4(2)+4(3) \dots 4(n) = 2n(n+1)$

edited Apr 14 '21 at 23:49

JMoravitz

asked Apr 14 '21 at 23:37

Benny

5

Where's the problem? – Matthew H. Apr 14 '21 at 23:39
sorry new user, i edited it – Benny Apr 14 '21 at 23:43
5

It looks like you've already solved the problem satisfactorily. What exactly is your question? – Cardboard Box Apr 14 '21 at 23:46
@CardboardBox well for the outer sigma, I just reasoned it logically but I was wondering if you guys can give me the proof as to why 4(1)+4(2)+4(3)…4(n)=2n(n+1) – Benny Apr 14 '21 at 23:48
3

Do you know what $1+2+\cdots n$ is? – kingW3 Apr 14 '21 at 23:49
oh, I see this all makes sense now, thank you all for the quick help. – Benny Apr 14 '21 at 23:51

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