Which expression gives the same result as ∑4i=0(5)(1/3)i?

The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign. So in the expression ∑4i = 0(5)(1/3)i will be the same as:

∑4i = 0(5)(1/3)i

= (1/3)⁰ + (1/3)¹ + (1/3)² + (1/3)³ + (1/3)⁴ + (1/3)⁵

= 364/243

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