Question

progression series x=1/80(41) + 1/79(42) + 1/78(43)..... + 1/41(80) and y=1-1/2+1/3-1/4+1/5......+1/79 - 1/80 solve for y/x

Answer 1

y/x=ln2/43.1193=0.0161

Answer 2

firstly, whaaaaaaaaaaaaat ? How did you solve that ?
Secondly, answer is wrong..

Answer 3

If you are not sure, calculate it manually, you will get the same result.
I know that you won't try. Just in case

Answer 4

@3mar How did you get that?

Answer 5

To be honest, I did it manually.
Do it yourself, you get what I got.

Answer 6

lol

Answer 7

Can you?

Answer 8

No, explain to me

Answer 9

Sorry dude... you wont get the answer as what you got... the answer is 60.5

Answer 10

Can you explain how did you get the answer, Mr niksbhalla14mar?

Answer 11

sure... if you say please...

Answer 12

@3mar

Answer 13

Please find the attacched solution @3mar

Answer 14

What about this?

Answer 15

y series

Answer 16

Please see, i have solved the same. This is from logic... not from derived works..

We needed to find y/x , not y alone.

Answer 17

You got y=121 and I got it ln2
who is the correct?

Answer 18

y=ln 2 if terms are infinite.

Answer 19

So if it is not infinite, it becomes 121 toooo big is not it?

Answer 20

\[1-\left( \frac{ 1 }{ 2 }-\frac{ 1 }{ 3 } \right)-\left( \frac{ 1 }{ 4 }-\frac{ 1 }{ 5 } \right)-...\left( \frac{ 1 }{ 78 }-\frac{ 1 }{ 79 } \right)-\frac{ 1 }{ 80 } <1\]

Answer 21

x=1/(80*41) + 1/(79*42) + 1/(78*43) + ... + 1/(41*80)
x = 2 [1/(80*41) + 1/(79*42) + 1/(78*43) + ... + 1/(61*60)]

and
y=1 - 1/2 + 1/3 - 1/4 + .... + 1/79 - 1/80
y = (1 + 1/2 + 1/3 + .... + 1/79 + 1/80) - 2(1/2 + 1/4 + 1/6 + ... + 1/80)
y = (1 + 1/2 + 1/3 + .... + 1/79 + 1/80) - 2*1/2 (1 + 1/2 + 1/3 + ... + 1/40)
y = (1 + 1/2 + 1/3 + .... + 1/79 + 1/80) - (1 + 1/2 + 1/3 + ... + 1/40)
y = 1/41 + 1/42 + 1/43 + ... + 1/80
y = (1/41+1/80) + (1/42+1/79) + (1/43+1/78) + ... (1/60+1/61)
y = 121/(41*80) + 121/(42*79) + 121/(43*78) + ... + 121/(60*61)
y = 121 [1/(41*80) + 1/(42*79) + 1/(43*78) + ... + 1/(60*61)]

Thus,
y / x
= 121 [1/(41*80) + 1/(42*79) + 1/(43*78) + ... + 1/(60*61)]
divided by
2 [1/(80*41) + 1/(79*42) + 1/(78*43) + ... + 1/(61*60)]
= 121/2