Math Chapter Wise question with answer

Q01 The sum of the infinite series 1- 2 3 1 1 1 + - +...... 2 2 2 is English · Bihar (TRE 2.0)-2023 Q02 The sum value of the series sin p + x sin (p+q) + [(x2)/2!] sin (p+2q) +........ is English · DSE TGT 2019 Q03 The sum of the series 2 2 2 2 2 2 1.2 2.3 3.4... 1! 2! 3! + + + + + + + + + + + + is English · PGT 2010 Q04 The sum of the series 2 3 4 5 1 2 3 4 x x x x........ 2 3 4 5 + + + + + + + + + + + + + + + + is (where |x| <1) English · PGT 2010 Q05 If |x|<1, the sum of the infinite series 2 3 4 1! 1 2! 1 3! 1.... 2! 3! 4! + + + + + + + + + + + + + + + + + + + +... English · PGT 2005 Q06 Sum to infinity of the series 2 3 4 1 2 1 2.... 7 7 7 7 + + + + + ∞ + + + + + ∞ + + + + + ∞ + + + + + ∞ is: English · PGT 2005