Respuesta :
Answer:
The value of [tex]0.98^5[/tex] is 0.9039207968.
Step-by-step explanation:
We need to find the value of [tex]0.98^5[/tex].
According to the binomial theorem,
[tex](a+b)^n=^nC_0a^n+^nC_{1}a^{n-1}b+...+^nC_{n-1}a^1b^{n-1}+^nC_nb^n[/tex]
Write 0.98 as a binomial: (1 - 0.02)
Write 0.98 as a binomial: (1 + (-0.02))
[tex]0.98^5=(1 + (-0.02))^5[/tex]
Using binomial theorem, we get
[tex]0.98^5=^5C_0(1)^5+^5C_1(1)^4(-0.02)^1+^5C_2(1)^3(-0.02)^2+^5C_3(1)^2(-0.02)^3+^5C_4(1)^1(-0.02)^4+^5C_5(1)^0(-0.02)^5[/tex]
[tex]0.98^5=(1)+5(-0.02)^1+10(-0.02)^2+10(-0.02)^3+5(-0.02)^4 +1(-0.02)^5[/tex]
[tex]0.98^5=(1)+(-0.1)+(0.004)+(-0.00008)+0.0000008+(-0.0000000032)[/tex]
[tex]0.98^5=0.9039207968[/tex]
Therefore the value of [tex]0.98^5[/tex] is 0.9039207968.
