Question

If S_n = $y = f(x)$ and $x = y$a_n = a, then$f:R \rightarrow R,f(x) = (x + 1)^{2}g:R \rightarrow R,g(x) = x^{2} + 1,$ is equal to-

• A. 0
• B. a
• C. $x = 0 \Rightarrow f(x) = 0$a
• D. 2a

Answer 1

Answer: (A)

0

Answer 2

S_n = a₁ + a₂ + …..+ a_n

S_n+1 = a₁ + a₂ +……+ a_n + a_n+1 ⇒ S_n+1 –S_n = a_n+1

$\frac { a _ { n + 1 } } { \sqrt { \frac { \mathrm { n } ( \mathrm { n } + 1 ) } { 2 } } }$

Q $\lim _ { n \rightarrow \infty }$ a_n = a

∴ $\lim _ { n \rightarrow \infty }$ a_n+1 = a

= $\frac { \mathrm { a } } { \alpha }$ = 0