Question

The sum of the series

1 + 2 $\left( 1 + \frac { 1 } { \mathrm { n } } \right) + 3 \left( 1 + \frac { 1 } { \mathrm { n } } \right) ^ { 2 }$ +...........¥ is given by –

• A. n²
• B. n² + 1
• C. n² –1
• D. None of these

Answer 1

Answer: (A)

n²

Answer 2

S = 1 + 2r + 3r² + 4r³.......

S_r = r + 2r² + 3r²......

S(1 – r) = 1 + r + r² ........

S = $\frac { 1 } { ( 1 - r ) ^ { 2 } }$ = $\frac { 1 } { \left( 1 - 1 - \frac { 1 } { n } \right) ^ { 2 } }$̃ S = n²