recursive equation doubt

Question

somewhere at the end solving a recursive equation we get like - 

2^n+2^n-1+2^n-2+......+2^0

Someone please simplify in layman terms how come from 2^0 to 2^n we have (n+1) terms?

Comments

2^n+2^n-1+2^n-2+......+2^0

=2^0+2^1+2^2+......+2^n-1+2^n

it is a simple g.p. series

{1+2⁽ⁿ⁺¹⁾}/(2-1)

1+2ⁿ⁺¹

Answer 1

See, write 2 terms------------------ 2^1+2^2               -----------------------(a)

now write 3 terms------------------- 2^1+2^2+2^3            -----------------------(b)

NOw,write n terms------------------  2^1+2^2+2^3.......+2^n  ---------------------- (c)   

See,

IF i ask, how many terms for equation (a),you will say 2 terms.

IF i ask, how many terms for equation (b),you will say 3 terms.

IF i ask, how many terms for equation (c),you will say n terms.

NOW IN  equation C add one more term 2^0,it will be (n+1) terms

I hope its clear now.

Comments

Nailed it, Angkit. :)

---

Thank you @iarnav :-)