Question

Which expression gives the same result as the shown image?

Answer 1

Answer:

Option B

Step-by-step explanation:

Summations have a property that says that if a constant term is multiplying the variable expression, it can be "removed" from the summation and placed on the left side of the operator, multiplying the entire expression. This is written as follows.

$\sum{(b(\frac{1}{k})^{i}) = b\sum{(\frac{1}{k})^{i}$

Now observe that the expression shown in the picture the only constant term used to multiply the expression is 5.

Thus:

$\sum{(5(\frac{1}{3})^{i}) = \sum{5(\frac{1}{3})^{i}\\\\= 5\sum{(\frac{1}{3})^{i}$

Finally the answer is Option B $5\sum{(\frac{1}{3})^{i}$

Answer 2

Answer:

The correct answer is option B.

Step-by-step explanation:

It is given that , a sum of terms.

Here only t value is changed.

The value of t is applicable only to the fraction 1/3. 5 is multiplied with each term inside the sigma.

Therefore we can take 5 out side the sum.

find the value of (1/3)^t  for t = 0 to 4 and add all terms. Then multiply it with 5.

Therefore the correct answer is option B