Find the value of Sn+1 – 3Sn + 3Sn-1 – Sn-2.
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ANSWER
S
n+3
−3 S
n+2
+3 S
n+1
−S
n
=(S
n+3
−S
n+2
)−2(S
n+2
−S
n+1
)+(S
n+1
−S
n
)
=(T
n+3
)−2(T
n+2
)+(T
n+1
) [In AP series, S
n+3
−S
n+2
=T
n+3
]
=T
n+3
−2{(T
n+1
+T
n+3
)÷2}+T
n+1
=T
n+3
−T
n+1
−T
n+3
+T
n+1
=0
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