MATH SOLVE

2 months ago

Q:
# For the geometric series given by 5 + 10 + 20+ . . . , which of the following statements is FALSE?None of the other 3 statements here are False.S₅₀₀ > S₄₉₉S₅₀₀ > a₅₀₀S1 = a1

Accepted Solution

A:

Answer:All statements are trueStep-by-step explanation:1. The statement [tex]S_{500}>S_{499}[/tex] is true, because [tex]S_{499}[/tex] is the sum of first 499 terms, [tex]S_{500}[/tex] is the sum of first 500 terms, and all these terms are positive, then the sum of smaller number of terms is less than the sum of larger number of terms.2. The statement [tex]S_{500}>a_{500}[/tex] is true, because [tex]S_{500}[/tex] is the sum of first 500 terms, [tex]a_{500}[/tex] is 500th term and the sum of 500 terms is greater than the 500th term.3. The statement [tex]S_1=a_1[/tex] is true, because [tex]S_1[/tex] is the sum of first 1 term that is exactly [tex]a_1.[/tex]All statements are true.