MCQ
$1+\frac{{{1}^{3}}+{{2}^{3}}}{2}+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}{3}+....+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+....+{{20}^{3}}}{20}=........$
- A$25025$
- B$12460$
- ✓$\frac{25025}{2}$
- D$\frac{22155}{2}$
$t_r=\frac{1^3+2^3+3^3+....+r^3}{r}$
$=\frac{r^2(r+1)^2}{4r}$
$\frac{r(r^2+2r+1)}{4}$
$=\frac{r^3+2r^2+r}{4}$
હવે , $1+\frac{1^3+2^3}{2}+\frac{1^3+2^3+3^3}{3}+......+ \frac{1^3+2^3+3^3+.....+20^3}{20}$
$=\frac{1}{4}\sum_{n=1}^{20}(r^3+2r^2+r)$
$=\frac{1}{4}$ $[$ સાદુરૂપ આપો $]$
$=\frac{25025}{2}$
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