Question

：0

想求這題用二項式定理解題的過程

(x-1)49 +1
(3) lim
x→0
X
||
49.
山
h=

Answer 1

qn

(x-1)⁴⁹ = x⁴⁹ - 49x⁴⁸ + ⋯ - C⁴⁹₂x² + 49x - 1

(x-1)⁴⁹+1 = x⁴⁹ - 49x⁴⁸ + ⋯ - C⁴⁹₂x² + 49x
= x ( x⁴⁸ - 49x⁴⁷ + ⋯ - C⁴⁹₂x + 49 )

[(x-1)⁴⁹+1] / x = x⁴⁸ - 49x⁴⁷ + ⋯ - C⁴⁹₂x + 49
右式代入 x=0，得 49