2 definitions by weirdnameith

2097152

2097152 is the 21th power of 2.

2097152 is an even number.
2097152 has a representation as a sum of 2 squares:
(2097152 = 1024² + 1024²)
A regular 2097152-gon is constructible with straightedge and compass.
Binary form: 1000000000000000000000₂.
Number length: 7 decimal digits.

Residues modulo small integers
m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
2097152 mod m | 0 | 2 | 0 | 2 | 2 | 1 | 0 | 8

Comparison:
≈ 0.57 × the number of arrangements of a 2×2×2 Rubik's cube ( 3.7×10^6).

Number of distinct prime factors ω(n): 1.
2097152 squared (20971522) is 4398046511104.
2097152 cubed (20971523) is 9223372036854775808.
2097152 is a perfect cube number. Its cube root is 128.

Person 1: Hey what is the answer to 2*2^4*8^2*2^2(2+2)*2(2^2)*2^2*2?
Person 2: Sure! the answer is 2097152!
Person 1: Thanks!
Person 2: No problem!

by weirdnameith August 5, 2023

0.92067359420779231894541352271649960

An example of an infinite sum.

∞

x e

∑ ─ = ──── = 0.92067359420779231894541352271649960...

eˣ (e-1)²

x=0

This sum converges.

--TESTS--
|convergence tests| result |
| ratio |series converges absolutely|
| root |series converges absolutely|
| integral |series converges absolutely|
| limit |(inconclusive) |

--Partial sum formula--

∞

x e⁻ⁿ(-en+n+eⁿ⁺¹-e)

∑ ─ = ───────────

eˣ (e-1)²

x=0

Alternate form:

1 1
─────+───── = 0.92067359420779231894541352271649960...

(e-1)² e-1

Person 1: Hey what does 1/(e-1)²+1/e-1?
Person 2: Sure! It's:"0.92067359420779231894541352271649960".
Person 1: Thanks!

by weirdnameith September 14, 2023