There is an averaging formula, one of many:
161[16a+15b+10c+3d], where the a, b, c, d are the consecutive terms of a slowly converging
alternating series.
π/4≈161[16(1)+15(−1/3)+10(1/5)+3(−1/7)]
π≈3.1428...
You can apply this to 1 - 1/2 + 1/3 - 1/4 to estimate ln(2), or log(2), if you prefer writing it that way, to give it
to two correct rounded decimal places.
Examples of others that it may be used on:
1/12−1/22+1/32−1/42
11−21+31−41
161[16a+15b+10c+3d], where the a, b, c, d are the consecutive terms of a slowly converging
alternating series.
π/4≈161[16(1)+15(−1/3)+10(1/5)+3(−1/7)]
π≈3.1428...
You can apply this to 1 - 1/2 + 1/3 - 1/4 to estimate ln(2), or log(2), if you prefer writing it that way, to give it
to two correct rounded decimal places.
Examples of others that it may be used on:
1/12−1/22+1/32−1/42
11−21+31−41
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