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

Explanation:

Answer 2

`\sum _(n=1)^4n+4=26`

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=(1)/(2)n\left(n+1\right)`

Here, n = 4, we get,

`=(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`