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Question

Let the series be 121+12+221+2+12+22+321+2+3+. Then

(where Tn and Sn denote the nth term and sum upto nth term respectively.)

A
Tn=2n+33
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B
Sn=n(n+2)3
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C
S31=420
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D
T31=21
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Solution

The correct options are
B Sn=n(n+2)3
D T31=21
Tn=12+22++n21+2++n
=n(n+1)(2n+1)6n(n+1)2
=n(n+1)(2n+1)3n(n+1)
=13(2n+1)
T31=21

Sn=nr=1Tr =nr=1[13(2r+1)]
=(23nr=1r)+13nr=11 =23n(n+1)2+n3 =13n(n+1)+n3

Sn=n(n+2)3
S31=31×333=341

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