Statement 1 : The sum of the series $1+(1+2+4)+$ $(4+6+9)+(9+12+16)+\ldots+(361+380+400)$ is 8000 .\

Question

Statement 1 : The sum of the series $1+(1+2+4)+$ $(4+6+9)+(9+12+16)+\ldots+(361+380+400)$ is 8000 .\ Statement $2: \sum_{k=1}^{n}\left(k^{3}-(k-1)^{3}ight)=n^{3}$ for any natural number $n$.\

Professor PC Thomas Classes · Answer

(d) : Statement 1: $1+(1+2+4)+$ $(4+6+9)+\ldots .+(361+380+400)$ is 8000\ $T_{1}=1, T_{2}=7=8-1$,\ $T_{3}=19=27-8$\ $\Rightarrow \quad T_{n}=n^{3}-(n-1)^{3}$\ Statement 2: $\sum_{k=1}^{n}\left(k^{3}-(k-1)^{3}ight)=n^{3}$\ $	herefore \quad$ Statement 2 is a correct explanation of statement 1 .\