Series help??? (1 Viewer)

[cerebrum]

Can someone help me with this question?

Evaluate the sum of the first 20 terms of the series
3 + 5 + 9 + 17 + 33 + 65 +....
(hint: 3= 2+1, 5= 4+1 and so on)


Can someone give me full working out??

 

[Dreamerish*~]

T_n = 2ⁿ + 1

S_n = (2¹ + 1) + (2² + 1) + (2³ + 1) + (2⁴ + 1) + ... + (2ⁿ + 1)

S₂₀ = (2¹ + 1) + (2² + 1) + (2³ + 1) + (2⁴ + 1) + ... + (2²⁰ + 1)

= 2¹ + 1 + 2² + 1 + 2³ + 1 + 2⁴ + 1 + ... + 2²⁰ + 1

= 2¹ + 2² + 2³ + 2⁴ + ... + 2²⁰ + 20

= 2 + 4 + 8 + 16 + ... + 1048576 + 20

= (^{2(220 - 1)}/_{2 - 1})* + 20

= 2097170

* The formula for the sum of geometric series. a = 2, n = 20 and r = 2.)

There you go.

Okay, since I helped you do this question, can you delete the post where you quoted my first attempt? I'm ashamed of it.

 

[cerebrum]

Thanks for the help.