Question
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Answer
$ S =1+2+4+7+\ldots . .+ T _{ n }$
$S =1+2+4+\ldots \ldots$
$Tn =1+1+2+3+\ldots . .+\left( T _{ n }- T _{ n -1}\right)$
$T _{ n }=1+\left(\frac{ n -1}{2}\right)[2+( n -2) \times 1]$
$T _{ n }=1+1+\frac{ n ( n -1)}{2}$
$n =100 T_{ n }=1+\frac{100 \times 99}{2}=4950+1$
$ n =101 T_{ n }=1+\frac{101 \times 100}{2}=5050+1=5051$
$n =102 T_{ n }=1+\frac{102 \times 101}{2}=5151+1=5152$
$n =103 T_{ n }=1+\frac{103 \times 102}{2}=5254$
$n =104 T_{ n }=1+\frac{104 \times 103}{2}=5357$
$S =1+2+4+\ldots \ldots$
$Tn =1+1+2+3+\ldots . .+\left( T _{ n }- T _{ n -1}\right)$
$T _{ n }=1+\left(\frac{ n -1}{2}\right)[2+( n -2) \times 1]$
$T _{ n }=1+1+\frac{ n ( n -1)}{2}$
$n =100 T_{ n }=1+\frac{100 \times 99}{2}=4950+1$
$ n =101 T_{ n }=1+\frac{101 \times 100}{2}=5050+1=5051$
$n =102 T_{ n }=1+\frac{102 \times 101}{2}=5151+1=5152$
$n =103 T_{ n }=1+\frac{103 \times 102}{2}=5254$
$n =104 T_{ n }=1+\frac{104 \times 103}{2}=5357$
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