Respuesta :
Answer:
[tex]\sum _{n=1}^4n+4=26[/tex]
Step-by-step explanation:
Given : [tex]\sum _{n=1}^4\:n+4[/tex]
We have to evaluate the sum.
Consider , the given sum [tex]\sum _{n=1}^4\:n+4[/tex]
Apply the sum rule, [tex]\sum a_n+b_n=\sum a_n+\sum b_n[/tex]
we have,
[tex]=\sum _{n=1}^4n+\sum _{n=1}^44[/tex]
Consider [tex]\sum _{n=1}^4n[/tex] first,
Applying sum formula, [tex]\sum _{k=1}^nk=\frac{1}{2}n\left(n+1\right)[/tex]
Here, n = 4, we get,
[tex]=\frac{1}{2}\cdot \:4\left(4+1\right)[/tex]
[tex]\sum _{n=1}^4n=10[/tex]
Now consider [tex]\sum _{n=1}^44[/tex]
[tex]\mathrm{Apply\:the\:Sum\:Formula:\quad }\sum _{k=1}^n\:a\:=\:a\cdot n[/tex]
[tex]=4\cdot \:4=16[/tex]
Therefore, [tex]=\sum _{n=1}^4n+\sum _{n=1}^44=10+16=26[/tex]
Thus, [tex]\sum _{n=1}^4n+4=26[/tex]
Answer: The quick check answers
1. B 2. B 3. B 4. C 5. A
Step-by-step explanation:
