What is the value of the summation $$\Sigma i =14(2i +6i2)$$ ?

A)180

B)200

C)220

D)240

Question

What is the value of the summation $$\Sigma i =14(2i +6i2)$$ ?

A)180

B)200

C)220

D)240

anonymous · Answer

@phi

phi · Answer

can you use the equation editor?

anonymous · Answer

that didnt come out right

anonymous · Answer

$$\Sigma i =14(2i +6i2)$$

anonymous · Answer

that is what it's supposed to be

phi · Answer

that does not make sense.  summations have a start and end value
for example
$$\sum_{i=1}^{3}i= 1+2+3$$

anonymous · Answer

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

anonymous · Answer

thats the real equation

phi · Answer

ok , write it like this $$2\sum_{i=1}^{4} i+6\sum_{i=1}^{4} i^{2} $$ there are "closed-form" solutions to these summations https://en.wikipedia.org/wiki/Triangular_number https://en.wikipedia.org/wiki/Square_pyramidal_number#Formula

phi · Answer

or, with only 4 terms, you could do it "by hand"

phi · Answer

the first summation is the sum of 1 to 4
then multiply that sum by 2

the second summation is the sum of the first four squares 1,4,9,16
I assume you can add those up.
then multiply by 6

finally, add the two different numbers for the combined answer

anonymous · Answer

Thanks so much @phi you da best