Series and Sequences (1 Viewer)

[0hNivlek]

5. 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)

* Copied directly from Maths in Focus.


Damn, i'm stuck on this review question ;x.

Thanks.

 

[gurmies]

2+1 (3) + 4 + 1 (5) + 8 + 1(9) + 16 + 1 (17) + 32 + 1 (33) + 64 + 1 (65)...

.'. S_20 = a(r^n -1)/(r-1) + 20

= 2(2^20-1) + 20

= 2,097,170

 

[Drongoski]

S = ( 2 + 4 + 8 + . . . + 2^20 ) + ( 1 + 1 + . . . + 1)

= 2(2^20 - 1)/(2-1) + 20 x 1

= 2^21 - 2 + 20

= 2097170

 

[0hNivlek]

Woah, i didn't know i could have separated all those 1's. Thanks !!