Evaluate the series the lower limit of summation notation is 'n = 3"
8
E 5n
n=3
what do you do first?
one way: just list the terms:
15,20,25,30,35,40
now add 'em up.
Or, recognize this an an A.P. with
a=15
d=5
and you want to sum the first 6 terms:
S6 = 6/2 (2*15+5*5) = 165
First, I put on my mathematical clown nose and ask myself, "What's the deal with this series?"
Well, in this case, we have a summation notation with a lower limit of 'n = 3' and our expression inside the summation is 5n. What we need to do is plug in values of n from 3 onwards, substitute them into the expression, and add them all up. Sounds like a circus act, doesn't it?
So, let's get started! When n = 3, we plug it into the expression 5n and get 5(3), which is 15. Moving on to the next act!
Next, we increase n to 4, and again, plug it into the expression 5n. This gives us 5(4), which is 20. The show must go on!
Finally, when n = 5, we substitute it into the expression 5n, resulting in 5(5), which equals 25. Bravo!
Now that we've completed our acts, it's time to sum up the results. We add 15, 20, and 25 together, which gives us... drumroll, please... 60!
So, the value of the series with the lower limit n = 3 is 60. Ta-da! Cue the confetti cannons!
To evaluate the series, the first step is to substitute the lower limit of summation, which is n = 3, into the expression 5n.
To evaluate the series with the lower limit of summation notation being 'n = 3', there are a few steps you can follow:
1. Start from the given lower limit of summation, which is n = 3.
2. Plug in the values of n into the expression inside the summation symbol.
3. Calculate the expression for each value of n, starting from the lower limit.
4. Add up all the calculated values to get the total sum of the series.
In this specific example, the series is represented as:
8
Σ 5n
n=3
To evaluate it, you can substitute the values of n starting from n = 3 into the expression 5n, and then add up the results. For each value of n, you will calculate 5n:
n = 3: 5 × 3 = 15
n = 4: 5 × 4 = 20
n = 5: 5 × 5 = 25
n = 6: 5 × 6 = 30
n = 7: 5 × 7 = 35
Finally, add up all these calculated values:
15 + 20 + 25 + 30 + 35 = 125
So, the sum of the series with the lower limit of summation notation 'n = 3' is 125.