SERIESSUM

Microsoft publishes =SERIESSUM(A3,0,2,A4:A7) = 0.707103 ("Approximation to the cosine of Pi/4 radians, or 45 degrees"). DERIVATION: the documented series is sum over i of coefficient_i * x^(n + (i-1)*m), here x = 0.785398163, n = 0, m = 2 and four coefficients, i.e. 1 - x^2/2 + x^4/24 - x^6/720. Evaluated at 50 digits on the ROUNDED LITERALS THE PAGE ACTUALLY PUTS IN THE CELLS -- 0.785398163, 1, -0.5, 0.041666667, -0.001388889, not PI()/4 and not -1/FACT(2) -- that is 0.7071032152046538649644, which is 0.707103 at the published precision. USING THE EXACT VALUES WOULD HAVE BEEN WRONG BY MORE THAN THE LAST PUBLISHED DIGIT: the page prints the same coefficients a second time as formulae (=PI()/4, =-1/FACT(2), =1/FACT(4), =-1/FACT(6)) in column B, and the true cos(0.785398163) is 0.7071067814675859, which differs from the series value in the SIXTH decimal (0.707107 vs 0.707103). The case therefore cites column A, the column the published formula reads. Microsoft's page was read live on 2026-08-31 at https://support.microsoft.com/en-us/excel/functions/seriessum-function. FETCH NOTE FOR THIS BATCH: batch F recorded every /en-us/office/<name>-function-<guid> URL returning Microsoft's 'Sorry, the page you're looking for can't be found' body; today BOTH paths serve the article again -- the GUID form redirects to /en-us/excel/functions/<slug>-function -- and every page cited in this batch came back complete (217-223 KB) in one or two attempts, with no 87 KB stub responses. Nothing here is sourced from a search snippet or a mirror.

Asserted at ten places from the derivation: 0.7071032152. This is the case that separates SERIESSUM from COS: at six published decimals the truncated series and the true cosine differ by 4e-6, which is visible but small; at ten places they differ in the sixth digit and cannot be confused.

With x = 2, n = 0, m = 1 and four unit coefficients the documented sum is 2^0 + 2^1 + 2^2 + 2^3 = 15 exactly. A structural assertion that pins down all three of the exponent arguments at once: an engine that started the power at n = 1, or stepped by m = 2, or reversed the coefficient order would return 30, 85 or 15 respectively -- the last is why the coefficients are all 1 here and NOT all 1 in the next case.

With x = 10, n = 0, m = 1 and coefficients 1, 2, 3 the documented sum is 1*10^0 + 2*10^1 + 3*10^2 = 1 + 20 + 300 = 321 exactly. Base ten makes the coefficient order readable straight off the answer: an engine applying them in reverse would return 123. No derived constant.

The page's only Remark publishes: "If any argument is nonnumeric, SERIESSUM returns the #VALUE! error value."

Microsoft publishes =SERIESSUM(A3,0,2,A4:A7) = 0.707103 ("Approximation to the cosine of Pi/4 radians, or 45 degrees"). DERIVATION: the documented series is sum over i of coefficient_i * x^(n + (i-1)*m), here x = 0.785398163, n = 0, m = 2 and four coefficients, i.e. 1 - x^2/2 + x^4/24 - x^6/720. Evaluated at 50 digits on the ROUNDED LITERALS THE PAGE ACTUALLY PUTS IN THE CELLS -- 0.785398163, 1, -0.5, 0.041666667, -0.001388889, not PI()/4 and not -1/FACT(2) -- that is 0.7071032152046538649644, which is 0.707103 at the published precision. USING THE EXACT VALUES WOULD HAVE BEEN WRONG BY MORE THAN THE LAST PUBLISHED DIGIT: the page prints the same coefficients a second time as formulae (=PI()/4, =-1/FACT(2), =1/FACT(4), =-1/FACT(6)) in column B, and the true cos(0.785398163) is 0.7071067814675859, which differs from the series value in the SIXTH decimal (0.707107 vs 0.707103). The case therefore cites column A, the column the published formula reads. Microsoft's page was read live on 2026-08-31 at https://support.microsoft.com/en-us/excel/functions/seriessum-function. FETCH NOTE FOR THIS BATCH: batch F recorded every /en-us/office/<name>-function-<guid> URL returning Microsoft's 'Sorry, the page you're looking for can't be found' body; today BOTH paths serve the article again -- the GUID form redirects to /en-us/excel/functions/<slug>-function -- and every page cited in this batch came back complete (217-223 KB) in one or two attempts, with no 87 KB stub responses. Nothing here is sourced from a search snippet or a mirror.

Asserted at ten places from the derivation: 0.7071032152. This is the case that separates SERIESSUM from COS: at six published decimals the truncated series and the true cosine differ by 4e-6, which is visible but small; at ten places they differ in the sixth digit and cannot be confused.

With x = 2, n = 0, m = 1 and four unit coefficients the documented sum is 2^0 + 2^1 + 2^2 + 2^3 = 15 exactly. A structural assertion that pins down all three of the exponent arguments at once: an engine that started the power at n = 1, or stepped by m = 2, or reversed the coefficient order would return 30, 85 or 15 respectively -- the last is why the coefficients are all 1 here and NOT all 1 in the next case.

With x = 10, n = 0, m = 1 and coefficients 1, 2, 3 the documented sum is 1*10^0 + 2*10^1 + 3*10^2 = 1 + 20 + 300 = 321 exactly. Base ten makes the coefficient order readable straight off the answer: an engine applying them in reverse would return 123. No derived constant.

The page's only Remark publishes: "If any argument is nonnumeric, SERIESSUM returns the #VALUE! error value."

Microsoft publishes =SERIESSUM(A3,0,2,A4:A7) = 0.707103 ("Approximation to the cosine of Pi/4 radians, or 45 degrees"). DERIVATION: the documented series is sum over i of coefficient_i * x^(n + (i-1)*m), here x = 0.785398163, n = 0, m = 2 and four coefficients, i.e. 1 - x^2/2 + x^4/24 - x^6/720. Evaluated at 50 digits on the ROUNDED LITERALS THE PAGE ACTUALLY PUTS IN THE CELLS -- 0.785398163, 1, -0.5, 0.041666667, -0.001388889, not PI()/4 and not -1/FACT(2) -- that is 0.7071032152046538649644, which is 0.707103 at the published precision. USING THE EXACT VALUES WOULD HAVE BEEN WRONG BY MORE THAN THE LAST PUBLISHED DIGIT: the page prints the same coefficients a second time as formulae (=PI()/4, =-1/FACT(2), =1/FACT(4), =-1/FACT(6)) in column B, and the true cos(0.785398163) is 0.7071067814675859, which differs from the series value in the SIXTH decimal (0.707107 vs 0.707103). The case therefore cites column A, the column the published formula reads. Microsoft's page was read live on 2026-08-31 at https://support.microsoft.com/en-us/excel/functions/seriessum-function. FETCH NOTE FOR THIS BATCH: batch F recorded every /en-us/office/<name>-function-<guid> URL returning Microsoft's 'Sorry, the page you're looking for can't be found' body; today BOTH paths serve the article again -- the GUID form redirects to /en-us/excel/functions/<slug>-function -- and every page cited in this batch came back complete (217-223 KB) in one or two attempts, with no 87 KB stub responses. Nothing here is sourced from a search snippet or a mirror.

Asserted at ten places from the derivation: 0.7071032152. This is the case that separates SERIESSUM from COS: at six published decimals the truncated series and the true cosine differ by 4e-6, which is visible but small; at ten places they differ in the sixth digit and cannot be confused.

With x = 2, n = 0, m = 1 and four unit coefficients the documented sum is 2^0 + 2^1 + 2^2 + 2^3 = 15 exactly. A structural assertion that pins down all three of the exponent arguments at once: an engine that started the power at n = 1, or stepped by m = 2, or reversed the coefficient order would return 30, 85 or 15 respectively -- the last is why the coefficients are all 1 here and NOT all 1 in the next case.

With x = 10, n = 0, m = 1 and coefficients 1, 2, 3 the documented sum is 1*10^0 + 2*10^1 + 3*10^2 = 1 + 20 + 300 = 321 exactly. Base ten makes the coefficient order readable straight off the answer: an engine applying them in reverse would return 123. No derived constant.

The page's only Remark publishes: "If any argument is nonnumeric, SERIESSUM returns the #VALUE! error value."