How do I enter my first term and common ratio?

Replace the 3 and 2 in 3*2^i with your numeric first term and ratio. Keep From at 0 and Step at 1. For n terms, set To to n - 1; for example, five terms use To = 4. Parenthesize a negative ratio, such as 3*(-2)^i.

What happens when the ratio is 1?

Each term equals the first term. With expression 3*1^i from 0 to 4, the five terms sum to 15.

Does this calculate the infinite sum?

No. The upper bound must be a finite integer, and the result is only the partial sum of the displayed range. It does not determine convergence or an infinite-series value.

Which method does it use?

The expression is evaluated over the chosen integer indices. Verified integer terms within 9,007,199,254,740,991 in magnitude use exact integer accumulation, even when their total is larger. Fractional, larger or already-rounded terms use a compensated floating-point total. A geometric closed-form formula is not used.

Finite Geometric Series Summation Calculator

Add a finite geometric series whose terms share a common ratio. The calculator below opens on first term 3 and ratio 2: 3 + 6 + 12 + 24 + 48 = 93. Edit the numeric first term, ratio or upper bound to calculate your own series.

Sum93i from 0 to 4, step 1 · 5 terms · first 3, last 48

Expression

Index

From

Step

Sum

Terms

First term

Last term

3 + 6 + 12 + 24 + 48

Added 5 verified integer terms one at a time in exact integer arithmetic, so nothing is lost to rounding.

Write powers with ^, multiply with * or by writing 2i, and use brackets freely. Functions: abs, acos, asin, atan, cbrt, ceil, comb, cos, cosh, exp, fact, floor, ln, log, log10, log2, max, min, mod, pow, round, sign, sin, sinh, sqrt, tan, tanh, plus the constants pi and e. Here log is base 10 and ln is natural.

i from 1 to 100step 1
5,050
i^2 from 1 to 10step 1
385
Upper bound below lower5 down to 1
empty range, sum 0

What this is exact about. Exact for integer terms whose evaluation is verified within the safe-integer range (up to 9,007,199,254,740,991 in magnitude); integer totals can be larger. Recognized linear expressions with verified integer coefficients also use exact integer arithmetic. Larger or already-rounded terms use floating-point approximation, and a compensated running sum reduces rounding in additions. It evaluates a finite number of terms, capped at 100,000 with a cancel button, and the closed form is used where the sequence is arithmetic and its linear structure is recognized. It makes no claim about whether an infinite series converges.

Common questions

How do I enter my first term and common ratio?: Replace the 3 and 2 in 3*2^i with your numeric first term and ratio. Keep From at 0 and Step at 1. For n terms, set To to n - 1; for example, five terms use To = 4. Parenthesize a negative ratio, such as 3*(-2)^i.
What happens when the ratio is 1?: Each term equals the first term. With expression 3*1^i from 0 to 4, the five terms sum to 15.
Does this calculate the infinite sum?: No. The upper bound must be a finite integer, and the result is only the partial sum of the displayed range. It does not determine convergence or an infinite-series value.
Which method does it use?: The expression is evaluated over the chosen integer indices. Verified integer terms within 9,007,199,254,740,991 in magnitude use exact integer accumulation, even when their total is larger. Fractional, larger or already-rounded terms use a compensated floating-point total. A geometric closed-form formula is not used.

Exact for integer terms whose evaluation is verified within the safe-integer range (up to 9,007,199,254,740,991 in magnitude); integer totals can be larger. Recognized linear expressions with verified integer coefficients also use exact integer arithmetic. Larger or already-rounded terms use floating-point approximation, and a compensated running sum reduces rounding in additions. It evaluates a finite number of terms, capped at 100,000 with a cancel button, and the closed form is used where the sequence is arithmetic and its linear structure is recognized. It makes no claim about whether an infinite series converges.