Solve this problem
P+p²+p³+p⁴+p⁵+p⁶+p⁷)/(p⁻³+p⁻⁴+p⁻⁵+p⁻⁶+p⁻⁷+p⁻⁸+p⁻⁹)
Answers
Answer:
p
−3
+p
−4
+p
−5
+p
−6
+p
−7
+p
−8
+p
−9
p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
\underline{\textsf{To find:}}
To find:
\textsf{The value of}The value of
\mathsf{\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}}
p
−3
+p
−4
+p
−5
+p
−6
+p
−7
+p
−8
+p
−9
p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
\underline{\textsf{Solution:}}
Solution:
\textsf{Consider,}Consider,
\mathsf{\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}}
p
−3
+p
−4
+p
−5
+p
−6
+p
−7
+p
−8
+p
−9
p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
\textsf{Multiply both numerator and denominator by}\,\mathsf{p^{10}}Multiply both numerator and denominator byp
10
\mathsf{=\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}{\times}\dfrac{p^{10}}{p^{10}}}=
p
−3
+p
−4
+p
−5
+p
−6
+p
−7
+p
−8
+p
−9
p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
×
p
10
p
10
\mathsf{=\dfrac{(p+p^2+p^3+p^4+p^5+p^6+p^7)p^{10}}{p^7+p^6+p^5+p^4+p^3+p^2+p}}=
p
7
+p
6
+p
5
+p
4
+p
3
+p
2
+p
(p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
)p
10
\mathsf{=\dfrac{(p+p^2+p^3+p^4+p^5+p^6+p^7)p^{10}}{p+p^2+p^3+p^4+p^5+p^6+p^7}}=
p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
(p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
)p
10
\mathsf{=p^{10}}=p
10
\underline{\textsf{Answer:}}
Answer:
\mathsf{\dfrac{p+p^2+p^3+p^4+p^5+p^6+p^7}{p^{-3}+p^{-4}+p^{-5}+p^{-6}+p^{-7}+p^{-8}+p^{-9}}=p^{10}}
p
−3
+p
−4
+p
−5
+p
−6
+p
−7
+p
−8
+p
−9
p+p
2
+p
3
+p
4
+p
5
+p
6
+p
7
=p
10
Here's your answer mate
P+p²+p³+p⁴+p⁵+p⁶+p⁷
______________________
p⁻³+p⁻⁴+p⁻⁵+p⁻⁶+p⁻⁷+p⁻⁸+p⁻⁹
By using property
p¹+²+³+⁴+⁵+⁶+⁷
______________
p¹+²+³+⁴+⁵+⁶+⁷+⁸+⁹
p²⁸
_____
p-⁴²
p²⁰-(-⁴²)
= p-²⁸