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Sum Of First N Numbers Calculator

Work out sum of first n numbers instantly with clear inputs, formula shown and shareable results.

About Sum Of First N Numbers Calculator

Gauss's pairing trick sums 1 to n by pairing the first and last terms: each pair totals n + 1 and there are n/2 pairs, giving n(n + 1)/2.

Formula

Triangular sum

1 + 2 + … + n = n(n + 1) / 2

Worked example

With the default values below, Sum Of First N Numbers Calculator returns Sum of 1 to n of 5,050. Change any input above and every figure here is recalculated in your browser.

Inputs used

How many terms naccepts 1–100,000,000
100
Start counting from
1

Results

Sum of 1 to n
5,050
Sum of n terms from your start value
5,050
Last term when starting at 1
100
Average of the terms
50.500000

Step by step

  1. 1Values used
  2. 2Triangular sum
  3. 3Sum of 1 to n= 5,050
  4. 4Sum of n terms from your start value= 5,050
  5. 5Last term when starting at 1= 100
  6. 6Average of the terms= 50.500000

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is 1 + 2 + … + 100?

100 × 101 / 2 = 5050, the sum the young Gauss reportedly found in seconds.

Why is the average (n+1)/2?

Because the terms are evenly spaced, so the mean is the midpoint of the first and last term.

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Sum Of First N Numbers Calculator – Calculate Sum of 1 to n