Sums of Powers Formula

[danimc]

I can not figure out why this is false????

Find a formula for the sum y³?+y³?+?+y??.
y³?+y³?+?+y??=(1+y+?+y³³)+(y³?+y³?+?+y??)-(1+y+?+y³³)

=(1+y+?+y??)-(1+y+?+y³³)=((y??-1)/(y-1))-((y³?-1)/(y-1))

Check: Evaluate ?_{i=34}??y^{i} = {

-((y³?)/(y-1))+((y??)/(y-1)) if y?1
44 if y=1
?
-((y³?)/(y-1))+((y??)/(y-1))=((y??-1)/(y-1))-((y³?-1)/(y-1)) is true

Using factoring:
y³?+y³?+?+y??=y³?(1+y+y²+?+y?³)=y³?(((y??-1)/(y-1)))

Check: Evaluate ?_{i=34}??y^{i}= {

-((y³?)/(y-1))+((y??)/(y-1)) if y?1
44 if y=1
?
-((y³?)/(y-1))+((y??)/(y-1))=y³?(((y??-1)/(y-1))) is false

 

[Denis]

Can't follow what you're doing...

Anyhow, as example:
y^5 + y^6 + y^7 + ... + y^n = [y^(n+1) - y^5] / (y - 1)

Let y = 2 and n = 10 and you'll get 2016...

 

[saravananbs]

Find a formula for the sum y³?+y³?+?+y??.

method 1.
y³?+y³?+?+y??=(1+y+?+y³³)+(y³?+y³?+?+y??)-(1+y+?+y³³)

=(1+y+?+y??)-(1+y+?+y³³)

=((y??-1)/(y-1))-((y³?-1)/(y-1))

=(y[sup:2t24lgtl]78[/sup:2t24lgtl]-y[sup:2t24lgtl]34[/sup:2t24lgtl])/(y-1)
=(y[sup:2t24lgtl]44[/sup:2t24lgtl]-1)y[sup:2t24lgtl]34[/sup:2t24lgtl]/y-1

method 2.

y³?+y³?+?+y??=y³?(1+y+y²+?+y?³)

=y[sup:2t24lgtl]34[/sup:2t24lgtl](y[sup:2t24lgtl]44[/sup:2t24lgtl]-1)/y-1

both are equal.

 

[lookagain]

Find a formula for the sum y³?+y³?+?+y??.

method 1.
y³?+y³?+?+y??=(1+y+?+y³³)+(y³?+y³?+?+y??)-(1+y+?+y³³)

=(1+y+?+y??)-(1+y+?+y³³)

=((y??-1)/(y-1))-((y³?-1)/(y-1))

=(y[sup:2gt7z0pd]78[/sup:2gt7z0pd]-y[sup:2gt7z0pd]34[/sup:2gt7z0pd])/(y-1)
=(y[sup:2gt7z0pd]44[/sup:2gt7z0pd]-1)y[sup:2gt7z0pd]34[/sup:2gt7z0pd]/(y-1) \(\displaystyle . . . **\)

method 2.

y³?+y³?+?+y??=y³?(1+y+y²+?+y?³)

=y[sup:2gt7z0pd]34[/sup:2gt7z0pd](y[sup:2gt7z0pd]44[/sup:2gt7z0pd]-1)/(y-1) \(\displaystyle . . . **\)

both are equal.

\(\displaystyle **\)Missing parentheses were added above.

Note: I would recommend typing in larger text such as \(\displaystyle y^{34},\) and the like.
Any posters, your lines of work, particulary the exponents, are not very readable.

 

[mmm4444bot]

Am I the only one seeing a plethora of open-box symbols throughout the original post? :?