Video Transcript
The sum of four 𝑟 plus one from 𝑟
equals one to 12 plus the sum of four 𝑟 plus one from 𝑟 equals 13 to 25 is equal
to what. Is it (A) the sum of eight 𝑟 plus
two from 𝑟 equals one to 25, (B) the sum of four 𝑟 plus one squared from 𝑟 equals
one to 25, (C) the sum of four 𝑟 plus two from 𝑟 equals one to 25, or (D) the sum
of four 𝑟 plus one from 𝑟 equals one to 25?
In order to answer this question,
we will use the property of series that states that the sum of 𝑎 sub 𝑟 from 𝑟
equals one to 𝑚 plus the sum of 𝑎 sub 𝑟 from 𝑟 equals 𝑚 plus one to 𝑛 is equal
to the sum of 𝑎 sub 𝑟 from 𝑟 equals one to 𝑛. This holds when 𝑚 is less than
𝑛. From the expression given, we see
that the value of 𝑚 is 12. 𝑚 plus one is therefore equal to
13, which is the start value of our second summation. We can also see that 𝑛 is equal to
25 and 𝑎 sub 𝑟 is equal to four 𝑟 plus one. The expression on the left-hand
side of our equation is therefore equal to the sum of four 𝑟 plus one from 𝑟
equals one to 25. This means that the correct answer
from the four options is option (D).
