Some Special Series Maths - Some Special Series

• A
  $2^{\text{n}}-\text{n}-1$
• B
  $1-\frac{1}{2^{\text{n}}}$
• ✓
  $\text{n}-1-\frac{1}{2^{\text{n}}}$
• D
  ${2^{\text{n}}}-1$

Answer: C.

• A
  $\frac{\text{n}(\text{n}+1)}{2}$
• B
  $\frac{\text{n}(\text{n}+1)(2\text{n}+1)}{12}$
• ✓
  $\frac{\text{n}(\text{n}+1)}{4}$
• D
  none of these.

Answer: C.

• A
  $\frac{\text{n}(\text{n}+1)}{2}$
• B
  $2\text{n}(\text{n}+1)$
• ✓
  $\frac{\text{n}(\text{n}+1)}{\sqrt{2}}$
• D
  $1$

Answer: C.

• A
  $\text{an}^2+\frac{\text{b}^{\text{n}-1}-1}{\text{b}^{\text{n}-1}(\text{b}-1)}$
• ✓
  $\text{an}^2+\frac{\text{b}^\text{n}-1}{\text{b}^\text{n}(\text{b}-1)}$
• C
  $\text{an}^3+\frac{\text{b}^{\text{n}-1}-1}{\text{b}^{\text{n}}(\text{b}-1)}$
• D
  none of these.

Answer: B.

• ✓
  $121\big(\sqrt{6}+\sqrt{2}\big)$
• B
  $243\big(\sqrt{3}+1\big)$
• C
  $\frac{121}{\sqrt{3}-1}$
• D
  $242\big(\sqrt{3}-1\big)$

Answer: A.