• ← RealValuedNumberQ

Sum

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Sum[expr, {i, imin, imax}]

evaluates the discrete sum of expr with i ranging from imin to imax.

Sum[expr, {i, imax}]

same as Sum[expr, {i, 1, imax}].

Sum[expr, {i, imin, imax, di}]

i ranges from imin to imax in steps of di.

Sum[expr, {i, imin, imax}, {j, jmin, jmax}, ...]

evaluates expr as a multiple sum, with {i, ...}, {j, ...}, ... being in outermost-to-innermost order.

A sum that Gauss in elementary school was asked to do to kill time:

• • Sum[k, {k, 1, 10}]

The symbolic form he used:

• • Sum[k, {k, 1, n}]

A Geometric series with a finite limit:

• • Sum[1 / 2 ^ i, {i, 1, k}]

A Geometric series using Infinity:

• • Sum[1 / 2 ^ i, {i, 1, Infinity}]

Leibniz formula used in computing Pi:

• • Sum[1 / ((-1)^k (2k + 1)), {k, 0, Infinity}]

A table of double sums to compute squares:

• • Table[ Sum[i * j, {i, 0, n}, {j, 0, n}], {n, 0, 4} ]

Computing Harmonic using a sum

• • Sum[1 / k ^ 2, {k, 1, n}]

Other symbolic sums:

• • Sum[k, {k, n, 2 n}]

A sum with Complex-number iteration values

• • Sum[k, {k, I, I + 1}]

• • Sum[k, {k, Range[5]}]

• • Sum[f[i], {i, 1, 7}]

Verify algebraic identities:

• • Sum[x ^ 2, {x, 1, y}] - y * (y + 1) * (2 * y + 1) / 6

Non-integer bounds:

• • Sum[i, {i, 1, 2.5}]

• • Sum[i, {i, 1.1, 2.5}]

• • Sum[k, {k, I, I + 1.5}]