C-13-Q070mediumsingle_mcq

$\left(1 + 2 + 3 + \cdots + n\right)^{2} = ?$

a $1^{3} + 2^{3} + \cdots + n^{3}$
b $1^{2} + 2^{2} + \cdots + n^{2}$
c $\dfrac{n(n+1)(2n+1)}{6}$
d $n^{2}(n+1)$

ব্যাখ্যা

By the cube-sum identity, $\left(1+2+\cdots+n\right)^2=\left[\frac{n(n+1)}{2}\right]^2=1^3+2^3+\cdots+n^3$ . The square of the sum of natural numbers equals the sum of their cubes.

এই অধ্যায়ের আরও প্রশ্ন

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Finite Series — সব প্রশ্ন দেখুন (160টি) →

$\left(1 + 2 + 3 + \cdots + n\right)^{2} = ?$

1^{3} + 2^{3} + \cdots + n^{3}

1^{2} + 2^{2} + \cdots + n^{2}

\dfrac{n(n+1)(2n+1)}{6}

n^{2}(n+1)

ব্যাখ্যা

By the cube-sum identity, $\left(1+2+\cdots+n\right)^2=\left[\frac{n(n+1)}{2}\right]^2=1^3+2^3+\cdots+n^3$ . The square of the sum of natural numbers equals the sum of their cubes.

(1+2+3+⋯+n)2=?\left(1 + 2 + 3 + \cdots + n\right)^{2} = ?(1+2+3+⋯+n)2=?

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

(1+2+3+⋯+n)2=?\left(1 + 2 + 3 + \cdots + n\right)^{2} = ?(1+2+3+⋯+n)2=?

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

$\left(1 + 2 + 3 + \cdots + n\right)^{2} = ?$

$\left(1 + 2 + 3 + \cdots + n\right)^{2} = ?$