Evaluate the Summation sum from n=1 to 4 of (3/4)^n

Problem

(∑_n=1^4)(3/4)

Solution

1. Identify the terms of the summation by substituting the values n=1,2,3,4 into the expression (3/4)n

2. Write the expanded sum of the four terms.

(3/4)1+(3/4)2+(3/4)3+(3/4)4

3. Calculate the value of each power.

3/4+9/16+27/64+81/256

4. Find a common denominator to add the fractions, which is 256

192/256+144/256+108/256+81/256

5. Sum the numerators over the common denominator.

(192+144+108+81)/256

6. Simplify the resulting fraction.

525/256

Final Answer

(∑_n=1^4)(3/4)=525/256

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