Question

5 la puterea 100-4*5 la puterea 99-4*5 la puterea 98-….-4*5
Dau coroana va rog repede!!!!

Answer 1

5¹⁰⁰-4(5⁹⁹+5⁹⁸+...+5)=5

${5}^{100} -4 \times ( 5\times \frac{5 {}^{99} - 1} {4})$

=

${5}^{100} -4 \times ( \frac{ {5}^{100} - 5 }{4} )$

=

${5}^{100} - {5}^{100} + 5 = 5$

Answer 2

5¹⁰⁰-4*5⁹⁹-4*5⁹⁸-….-4*5

5¹⁰⁰-4(5⁹⁹+5⁹⁸+...+5)=E

S=5+5²+...+5⁹⁸+5⁹⁹

5S=-5+(5+5²+5³+...+5⁹⁹+5¹⁰⁰)

5S=-5+S+5¹⁰⁰

4S=5¹⁰⁰-5

S=(1/4)5¹⁰⁰-5/4

E=5¹⁰⁰-4[(1/4)5¹⁰⁰-5/4]=5¹⁰⁰-5¹⁰⁰+5=5