Calculate the sum of the first 'n' terms of a sequence.
Sequence Settings
Calculation Results
Partial Sum (Sn)55
nth Term (an)10
About this calculator
What is a Partial Sum?
The partial sum is the sum of a finite number of terms from a sequence. For an infinite series, the sequence of partial sums helps determine if the series converges or diverges.
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Pro Tips
Arithmetic sequences have a constant difference.
Geometric sequences have a constant ratio.
If |r| < 1, a geometric series converges as n approaches infinity.
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Fun Facts
"Young Carl Friedrich Gauss famously found the sum of the first 100 integers in seconds using the arithmetic sum pattern."
"The harmonic series (1 + 1/2 + 1/3 + ...) has partial sums that grow indefinitely, but very slowly."
Formula: Arithmetic: Sn = n/2(a₁ + an) | Geometric: Sn = a₁(1-rⁿ)/(1-r)
