What is the value of the summation #sum_(i=1)^4(2i + 6i^2)#?

Answer 1

#\sum_{i=1}^4 (2i+6i^2)=200#

Given we have to solve #\sum_{i=1}^4 (2i+6i^2)#
We have to first break open the sum into 2 parts, which will be #2\sum_{i=1}^4(i)+6\sum_{i=1}^4(i^2)# Since both #2# and #6# in their respective terms are constants that do not change, I've kept them out of the sum term.
Now, the question is easy. Of course we know that #\sum_{i=1}^ni=n(n+1)/2# and that #\sum_{i=1}^ni^2=n(n+1)(2n+1)/6# So substituting #n=4#, we get #\sum_{i=1}^4i=cancel{4}^2*5/cancel{2}=10# and #\sum_{i=1}^ni^2=cancel{4}^2*5*cancel{9}^3/cancel{6}^1=30#

Taking all that into their respective places, you'll see what the answer is.

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Answer 2

The value of the summation ( \sum_{i=1}^4 (2i + 6i^2) ) is 194.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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