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The sum of 1.03 + (1.03)2 + (1.03)3 + …. to n terms is
- a)103 {(1.03)n – 1}
- b)103/3 {(1.03)n – 1}
- c)(1.03)n –1
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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The sum of 1.03 + (1.03)2 + (1.03)3 + . to n terms isa)103 {(1.03)n 1...
Given sum is 1.03 + (1.03)^2 + (1.03)^3 + ... + (1.03)^n.
To find the formula for this sum, we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r)
where S is the sum of the geometric series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1.03 and r = 1.03, since each term is obtained by multiplying the previous term by 1.03. Thus, the formula for the sum is:
S = 1.03(1 - 1.03^n) / (1 - 1.03)
Simplifying this expression, we get:
S = 103/3 * (1.03^n - 1)
Therefore, the correct answer is option B: 103/3 * (1.03^n - 1).
To find the formula for this sum, we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r)
where S is the sum of the geometric series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1.03 and r = 1.03, since each term is obtained by multiplying the previous term by 1.03. Thus, the formula for the sum is:
S = 1.03(1 - 1.03^n) / (1 - 1.03)
Simplifying this expression, we get:
S = 103/3 * (1.03^n - 1)
Therefore, the correct answer is option B: 103/3 * (1.03^n - 1).
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The sum of 1.03 + (1.03)2 + (1.03)3 + . to n terms isa)103 {(1.03)n 1...
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