Question

FInd the $n^{th}$ term of the series $(1{)}^3$ + ($1^3$ + $2^3$) + ($1^3$ + $2^3$ + $3^3$) + ------------------- n terms.

• A. (n(n+1)(2n+1)) / 6
• B. (n(n+1)) / 2
• C. [(n(n+1)) / 2]²
• D. (n³(n+1)³) / 24

Answer 1

The correct option is C

[(n(n+1)) / 2]²

$(1{)}^3$ + ($1^3$ + $2^3$) + ($1^3$ + $2^3$ + $3^3$) + ------------------- n terms

$n^{th}$ of the series $T_n$ = $1^3$ + $2^3$ + $3^3$ + $4^3$ + -----------$n^3$

$T_n$ = ${\sum }_{i=1}^n{n}^3$ = $\frac{n^2(n+1{)}^2}{4}$