累乗根のテイラー展開

(1+x)^(1/ 2 )
=1+( 1/2 )*x+(-1/8 )*x^ 2 +( 1/16 )*x^ 3 +(-5/128 )*x^ 4 +( 7/256 )*x^ 5
+(-21/1024 )*x^ 6 +( 33/2048 )*x^ 7 +(-429/32768 )*x^ 8 ・・・・・・

(1+x)^(1/ 3 )
=1+( 1/3 )*x+(-1/9 )*x^ 2 +( 5/81 )*x^ 3 +(-10/243 )*x^ 4 +( 22/729 )*x^ 5
+(-154/6561 )*x^ 6 +( 374/19683 )*x^ 7 +(-935/59049 )*x^ 8 ・・・・・・

(1+x)^(1/ 4 )
=1+( 1/4 )*x+(-3/32 )*x^ 2 +( 7/128 )*x^ 3 +(-77/2048 )*x^ 4 +( 231/8192 )*x^ 5
+(-1463/65536 )*x^ 6 +( 4807/262144 )*x^ 7 +(-129789/8388608 )*x^ 8 ・・・・・・

(1+x)^(1/ 5 )
=1+( 1/5 )*x+(-2/25 )*x^ 2 +( 6/125 )*x^ 3 +(-21/625 )*x^ 4 +( 399/15625 )*x^ 5
+(-1596/78125 )*x^ 6 +( 6612/390625 )*x^ 7 +(-28101/1953125 )*x^ 8 ・・・・・・

(1+x)^(1/ 6 )
=1+( 1/6 )*x+(-5/72 )*x^ 2 +( 55/1296 )*x^ 3 +(-935/31104 )*x^ 4
+( 4301/186624 )*x^ 5 +(-124729/6718464 )*x^ 6 +( 623645/40310784 )*x^ 7
+(-25569445/1934917632 )*x^ 8 ・・・・・・

(1+x)^(1/ 7 )
=1+( 1/7 )*x+(-3/49 )*x^ 2 +( 13/343 )*x^ 3 +(-65/2401 )*x^ 4 +( 351/16807 )*x^ 5
+(-1989/117649 )*x^ 6 +( 81549/5764801 )*x^ 7 +(-489294/40353607 )*x^ 8 ・・・・・・

(1+x)^(1/ 8 )
=1+( 1/8 )*x+(-7/128 )*x^ 2 +( 35/1024 )*x^ 3 +(-805/32768 )*x^ 4
+( 4991/262144 )*x^ 5 +(-64883/4194304 )*x^ 6 +( 435643/33554432 )*x^ 7
+(-23960365/2147483648 )*x^ 8 ・・・・・・

(1+x)^(1/ 9 )
=1+( 1/9 )*x+(-4/81 )*x^ 2 +( 68/2187 )*x^ 3 +(-442/19683 )*x^ 4
+( 3094/177147 )*x^ 5 +(-68068/4782969 )*x^ 6 +( 515372/43046721 )*x^ 7
+(-3994133/387420489 )*x^ 8 ・・・・・・

(1+x)^(1/ 10 )
=1+( 1/10 )*x+(-9/200 )*x^ 2 +( 57/2000 )*x^ 3 +(-1653/80000 )*x^ 4
+( 64467/4000000 )*x^ 5 +(-1052961/80000000 )*x^ 6
+( 8874957/800000000 )*x^ 7 +(-612372033/64000000000 )*x^ 8 ・・・・・・

(1+x)^(1/ 11 )
=1+( 1/11 )*x+(-5/121 )*x^ 2 +( 35/1331 )*x^ 3 +(-280/14641 )*x^ 4
+( 2408/161051 )*x^ 5+(-21672/1771561 )*x^ 6 +( 201240/19487171 )*x^ 7
+(-1911780/214358881 )*x^ 8 ・・・・・・

(1+x)^(1/ 12 )
=1+( 1/12 )*x+(-11/288 )*x^ 2 +( 253/10368 )*x^ 3 +(-8855/497664 )*x^ 4
+( 83237/5971968 )*x^ 5 +(-4910983/429981696 )*x^ 6 +( 49811399/5159780352 )*x^ 7
+(-4134346117/495338913792 )*x^ 8 ・・・・・・