Question

(2) Wote: ( 7 mathrm{f}_{1}=+1 / sqrt{2}, mathrm{T}_{2} ) will be ( sqrt{frac{sqrt{2}-1}{2 sqrt{2}}} ) which is
smaller than T, i, It is an A ing A.P, SoT, ( 2 T_{1} )
[
begin{aligned}
text { Put } n={&, quad s_{1}=left(1+2 T_{1}right)left(1-T_{1}right) quad text { where } S_{1}=T_{1}
& therefore T_{1}=1-pi_{1}+2 pi_{1}-2 T_{1}^{2}
therefore & 2 T_{1}^{2}=1 Rightarrow T_{1}=pm frac{1}{sqrt{2}} Rightarrow text { Jabe } T_{1}=-1 / sqrt{2}
end{aligned}
]
as sn is increasing wroucte Ale. Put ( n=2, quad S_{2}=1-T_{2}+2 T_{2}-2 T_{2}^{2} ) where
[
begin{array}{c}
T_{1}+T_{2}=1+T / 2-2 T_{2}^{2}
2 T_{2}^{2}=1-T_{1} Rightarrow T_{2}^{2}=frac{1-left(frac{-1}{sqrt{2}}right)}{2}=frac{sqrt{2}+1}{2 sqrt{2}}(1)
end{array}
]

# 20. Sum of the first n terms of an A.P (having positive terms) is given by Sn=(1+212) (1 -TR) where T is the term of the series. The value of T2 is 12-1 (C) 252 (D) None of these 12+1 (A) 212 (B) 252

Solution