16 - The Geometric Series - Definition, Meaning & Examples - Part 1
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- เผยแพร่เมื่อ 3 ม.ค. 2025
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In this lesson, you will learn about the very important series known as the geometric series. The geometric series is a listing of terms that are added together whereby each term is obtained by multiplying the previous term by a common ratio. Essentially, we take the corresponding terms in the geometric sequence and take the sum by adding up all terms, thus arriving at the geometric series. We first write down the formula for the sum of the geometric series, then we explain exactly how the formula works. Finally, we use the geometric series formula to solve problems.
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So far so good 7 minutes in, going to resume the next part tomorrow. A lot of information to take in.
Sometimes, the sum formula for geometric series is written as sn=t1(r^n-1)/(r -1) to emphasize that r>1.
Subtraction of second equation from the first might confuse us. But, remember both the equations have the same number of terms, and the first term of equ1 and last term of equ2 turns out be unlike terms and they don't cancel and remain as difference.
One essence of our education is to prove or disprove our beliefs (misconceptions) so that we become more conscious about our thoughts and acts.
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I like your computation because it is clear to decipher.
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Sir may u pls explain why u did not align sn and rsn 12:37. I understand u want them to align but I have never heard a math rule were u shift values to left before subtracting them
such a great teacher. thank you!
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Hi Jason, would you cover Power Series in this unit?
Fantastic.
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lecture on sampling and sampling distribution plz need it
What's the name of the playlist guys
One video on precalculas please
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Thank you!
subtraction change sign
Thank you so much for sharing your knowledge.May God bless you
s8=1(1-128)/1-2
I think its a1 not t1 sir?
s8=(1-256)/-1=-255/-1
s10=2(-354293)/1-(-3)
s8=1(1-2 8)/1-2
sn=t1(1-rn)/1-r
1+2+4+6+8+16+32+64+128=255
s10=177146 remainder 2
s10=-177146 remainder 2
s10=2(1-(-3)10)/1-(-3)
add product
if the R is 1, you can do derivative of the r to n, and it proves your comment on n x t1 ;)
-39366(-3)
s10=-708586/4
More problems on Gp
s10 2(1-(-3)10/1-(-3)
r-3
-39366/-3
s8=127
r=-3 n=10 t1=2
2 7=128
1458/-3
255=255
t1=2
s10=531440
118098(-3)
162
64(2)
- 44286
-354294(-3)
18
Sn mean
-54
-486
n 8 r 2 t1=1
n10=354294
127
128
14762
I want to buy video lecture but I am poor boy I have nothing money . What shall I do Prof ?
n10
formula
1458
geometry
You're a fuckin genius !
Boeing and boeing
Hi
Hi!
It is not quite correct.
n10=-354294
-354294
531440
s8(1-128)/-1=127/-1
s10=2(1(-3)10)/1-(-3)
-4374/-3
-54/-3
162/-3
s8=255
-4374
s10=2(1-(-354294)/1-(-3)
formula
118098
s8=1(1-rn)/1-r
sn=t1(1-rn)/1-r
-486/-3
-39366
118098
13122