´root(4)(1+x) = sum_(n=0)^(oo) ((0.25), (n)) x^n´ für ´|x| < 1´

"´a ~~ 7.50 \* 10^(-7501)´\n\n´a = 10^2500 \* (1 - root 4 (1 + (-3) \* 10^(-10000)))´\n\n´x := -3 \* 10^(-10000)´\n\n´root 4 (1+x) = 1 + 1/4 x + (- 3/32)x^2 + R_2(x)´\n\n´=> a = 10^2500 (1 - (1 + 1/4 x - 3/32 x^2 + R_2(x)))´\n´= 10^2500(-1/4 x + 3/32 x^2 - R_2(x))´\n´= 10^2500(3/4 \* 10^(-10000) + 3/32 \* 9 \* 10^(-20000) - R_2(x))´\n´= 10^-7500(3/4 + 27/32 \* 10^(-10000) - R_2(x) \* 10^10000)´\n´= 10^-7501(7.5 + 8.4375 \* 10^(-10000) - R_2(x) \* 10^10001)´\n\n´R_2(x) = (f'''(z))/(3!) x^3´ (für ein z zwischen ´x´ und ´0´; ´x < z < 0´)\n\n´root 4 (1+x) = (1+x)^(1/4)´\n\n´f'(x) = 1/4(1+x)^(-3/4)´\n´f''(x) = 1/4 (-3/4) (1+x)^(-7/4)´\n´f'''(x) = 1/4 (-3/4) (-7/4) (1+x)^(-11/4)´\n\n´=> -R_2(x) 10^10001 = -10^(10001) \* 21/(64 \* 6) (1+z)^(-11/4) (-27) \* 10^(-30000)´\n´= 10^(-19999) 189/128 (1+z)^(-11/4)´\n´(1+z)^(-11/4) = 1/((1+z)^(11/4)) < 1/(0.9^(11/4)) < 2´\n\n´=> 0 < -R_2(x) \* 10^10000 < 189/64 \* 10^(-19999) < 3 \* 10^(-19999)´\n\n´a ~~ (7.5 + 8.4375 \* 10^(-10000) + 3 \* 10^(-19999)) \* 10^(-7501)´\n´~~ 750^9998 843750^8996 \* 10^(-7501)´"