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Question

Find the value of 13 + 23 + 33 +..... upto 8 terms -

The correct answer is

1296

Used Concept:

Sum of the cubes of natural numbers = = (n × (n + 1) / 2)2

Calculation:

In this case, n = 8 (since we want to find the sum of cubes up to 8 terms).

⇒ Sum = (8 × (8 + 1) / 2)2

⇒ Sum = (8 × 9/2)2

⇒ Sum = (4 × 9)2

⇒ Sum = 362

⇒ Sum = 1296

∴ The sum of the cubes of the first 8 natural numbers is 1296.

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Important Questions from Geometric Progressions

  1. If \(2^{\frac{1}{c}}, 2^{\frac{b}{a c}}, 2^{\frac{1}{a}}\) are in GP, then which one of the following is correct ?

  2. If G is the geometric mean of numbers 1, 2, 22, 23,.....2n-1, then what is the value of 1 + 2log2G ?

  3. If m is the geometric mean of \({\left( {\frac{{\rm{y}}}{{\rm{z}}}} \right)^{\log \left( {{\rm{yz}}} \right)}},{\rm{\;}}{\left( {\frac{{\rm{z}}}{{\rm{x}}}} \right)^{\log \left( {{\rm{zx}}} \right)}}{\rm{\;and\;}}{\left( {\frac{{\rm{x}}}{{\rm{y}}}} \right)^{\log \left( {{\rm{xy}}} \right)}}\) then what is the value of m?

  4. The value of the infinite product \({6^{\frac{1}{2}}} \times {6^{\frac{1}{2}}} \times {6^{\frac{3}{8}}} \times {6^{\frac{1}{4}}} \times \ldots \) is

  5. The geometric mean of the observations x 1, x 2, x 3, … x nis G 1. The geometric mean of the observations y 1, y 2, y 3,… y nis G 2. The geometric mean of observations \(\frac{{{{\rm{x}}_1}}}{{{{\rm{y}}_1}}},\frac{{{{\rm{x}}_2}}}{{{{\rm{y}}_2}}},\frac{{{{\rm{x}}_3}}}{{{{\rm{y}}_3}}}, \ldots \frac{{{{\rm{x}}_{\rm{n}}}}}{{{{\rm{y}}_{\rm{n}}}}}\) is

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