Solve for X in this Geometric Series without using Formula | Geometric Sequence Progression

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Solve for X in this Geometric Series without using Formula | Geometric Sequence Progression

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[nirupamasingh]

V nice Sir. A diff method v nice presentation.

[fevengr]

After looking for a minute I recognized the series as a binary number written backwards (LSB to MSB). Since (base 2) = 2047, then (base 2) = 2046 (which is consistent with the series implying a value of 0 for the 2^0 bit). In any case, the MSB = 2^10 = 1024. Admittedly a very convoluted solution but one that is consistent with my convoluted personality. 🙂

[adgfx]

2(2^n -1)=2046=>2^n no of terms=10.thus x=2^10=1024 ans

[timeonly]

This is the "trick" I learned to convert numbers with a repeating decimal tail into a fraction! This is also how the partial-sum formula for geometric sequences is derived. Nice example to show it all relates! :-).

[normanc]

Thank you for yout video. Doubling the sum then substracting it you get the first and last term. You are clever.

[SuperYoonHo]

Thank you sir!!!
I solved the same way as you did! You are awesome. God bless you richly

[philipkudrna]

I did it the „rough“ an less beautiful approach since it was clear that we are talking about only a limited number of items to be added. If you add 2+4+8+16+32+64+128+256+512 you get 1022. What‘s missing to 2046 is 1024. One could even identify a pattern (2+4=6, which is 2 less than „the next barrier“, similarly 6+8=14 (2 less than 16), so even without adding all the numbers up it becomes clear quickly that one arrives at 1022 (2 less than 1024).

[ferdaatila]

Do we not have a redundant x in eq.2? All values are double in eq.2 and x becomes 2x. Why do we have an extra x?

[HappyFamilyOnline]

Awesome solution👍
Thanks for sharing😊😊

[sivadanka]

Good work sir 👍
(2046/2)+ 1 can also give us the answer

[billcame]

When I saw the problem, the first thing that popped into my mind was your solution.

[owlsmath]

Good one! 😀 I looked at it like binary 2^11 - 2 = 2046 so choose 2^10

[oscarpauzerfilho]

Congrats Sir!!! Thank You Very Much for this wonderful explanation.👍👍👍👏👏👏

[wafikhwijeh]

Sir... I prefer to but x/2 befor x for mor cleaning, at tge given series, then we can delet it after understanding to justify. ( x + 2x ) at the end of series. Just my opinion. Thanks so much for you sir.

[predator]

Awesome problem with awesome solution 👍, thank you teacher 🙏.

[shashankkulkarni]

Sir you are brilliant in teaching mine maths skill is improved now

[math]

very well done bro, thanks so much for sharing

[TurquoizeGoldscraper]

Being a programmer, I recognized the powers of 2 and how they added up, so I got 1024 without thinking about it.

[randomjudgements]

It is a funny thing 😂
I solved it using geometric series formula
And after that I saw what you had written in the thumbnail 😂
Btw your method was cool 👍👍
Nice ☺️

[rangaswamyks]

Please explain
How you added
....
How x+2x sir?
When we multiply by 2
X becomes 2x thats it. M