Question

Evaluate the series 4 sigma n=1 n+4

Answer 1

Answer: The quick check answers

1. B 2. B 3. B 4. C 5. A

Step-by-step explanation:

Answer 2

Answer:

$\sum _{n=1}^4n+4=26$

Step-by-step explanation:

 Given : $\sum _{n=1}^4\:n+4$

We have to evaluate the sum.

 

Consider , the given sum $\sum _{n=1}^4\:n+4$

Apply the sum rule, $\sum a_n+b_n=\sum a_n+\sum b_n$    

we have,

$=\sum _{n=1}^4n+\sum _{n=1}^44$

Consider $\sum _{n=1}^4n$ first,

Applying sum formula, $\sum _{k=1}^nk=\frac{1}{2}n\left(n+1\right)$

Here, n = 4, we get,

$=\frac{1}{2}\cdot \:4\left(4+1\right)$

$\sum _{n=1}^4n=10$

Now consider $\sum _{n=1}^44$

$\mathrm{Apply\:the\:Sum\:Formula:\quad }\sum _{k=1}^n\:a\:=\:a\cdot n$

$=4\cdot \:4=16$

Therefore, $=\sum _{n=1}^4n+\sum _{n=1}^44=10+16=26$

Thus, $\sum _{n=1}^4n+4=26$