Question

11. Calculati : a = 5 ^100 - 4 x 5^98 -... - 4 x 5^50.​​

Answer 1

Răspuns:

Explicație pas cu pas:

a = 5¹⁰⁰ - 4·5⁹⁸-.....-4·5⁵⁰ = 5¹⁰⁰ - b

b = 4·5⁹⁸+4·5⁹⁶+..+4·5⁵⁰  = 4·5⁵⁰·(5⁴⁸+5⁴⁶+....+1) = 4·5⁵⁰·c

c = 5⁴⁸+5⁴⁶+....+1   I·5²  =>

25c = 5⁵⁰+5⁴⁸+.....+5² = 5⁵⁰+c -1 =>

24c = 5⁵⁰-1

b = 4·5⁵⁰·(5⁵⁰-1) = 4·5¹⁰⁰-4·5⁵⁰

a = 5¹⁰⁰-4·5¹⁰⁰+4·5⁵⁰

a = -3·5¹⁰⁰+4·5⁵⁰ = 5⁵⁰·(4 - 3·5⁵⁰)