Write a program to find the sum of the series : s=1+p+p2+p3+….+pn
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Answer:
We have I+p+p
2
+.....+p
n
=O ----------(1)
Since p is a nonsingular matrix, p is invertible.
Multiplying both sides of (1) by p
−1
, we get
p
−1
+I+Ip+.....+p
n−1
I=O.p
−1
or p
−1
+I(1+p+......+p
n−1
)=O
or p
−1
=−I(I+p+p
2
+.....+p
n−1
)=−I(−p
n
)=p
n
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