A) \[{{99.2}^{100}}\]
B) \[{{100.2}^{100}}\]
C) \[{{99.2}^{100}}+1\]
D) \[{{1000.2}^{100}}\]
E) \[{{100.2}^{100}}-1\]
Correct Answer: C
Solution :
Let \[S=1+2.2+{{3.2}^{2}}+{{4.2}^{3}}+....+{{100.2}^{99}}\]...(i) \[\therefore \] \[2S=1.2+{{2.2}^{2}}+{{3.2}^{3}}+....+{{100.2}^{100}}\] ...(ii) On subtracting Eq. (i) from (ii), we get \[-S=1+1.2+{{1.2}^{2}}+{{3.2}^{3}}+.....+{{1.2}^{99}}\] \[-{{100.2}^{100}}\] \[\Rightarrow \] \[-S={{2}^{100}}-1-{{100.2}^{100}}\] \[\Rightarrow \] \[S={{99.2}^{100}}+1\]
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