Theorem finite_geom_sum of type Forall

from the theory of proveit.numbers.summation

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.summation import finite_geom_sum

# check that the built expression is the same as the stored expression
assert finite_geom_sum.expr == stored_expr
assert finite_geom_sum.expr._style_id == stored_expr._style_id
print("Passed sanity check: finite_geom_sum matches stored_expr")

Passed sanity check: finite_geom_sum matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{x \in \mathbb{C}, n \in \mathbb{N}~|~x \neq 1}~\left(\left(\sum_{i = 0}^{n} x^{i}\right) = \frac{1 - x^{n + 1}}{1 - x}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	52, 56
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16
12	Operation	operator: 17 operand: 25
13	Operation	operator: 19 operands: 20
14	Operation	operator: 39 operands: 21
15	Operation	operator: 39 operands: 22
16	Operation	operator: 23 operands: 24
17	Literal
18	ExprTuple	25
19	Literal
20	ExprTuple	26, 27
21	ExprTuple	52, 28
22	ExprTuple	56, 29
23	Literal
24	ExprTuple	52, 57
25	Lambda	parameter: 44 body: 31
26	Operation	operator: 54 operands: 32
27	Operation	operator: 54 operands: 33
28	Literal
29	Literal
30	ExprTuple	44
31	Conditional	value: 34 condition: 35
32	ExprTuple	57, 36
33	ExprTuple	57, 37
34	Operation	operator: 49 operands: 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 42 operand: 46
37	Operation	operator: 42 operand: 52
38	ExprTuple	52, 44
39	Literal
40	ExprTuple	44, 45
41	ExprTuple	46
42	Literal
43	ExprTuple	52
44	Variable
45	Operation	operator: 47 operands: 48
46	Operation	operator: 49 operands: 50
47	Literal
48	ExprTuple	51, 56
49	Literal
50	ExprTuple	52, 53
51	Literal
52	Variable
53	Operation	operator: 54 operands: 55
54	Literal
55	ExprTuple	56, 57
56	Variable
57	Literal