Question

how many terms of the series1³+2³+3³+......should be taken to get the sum of 14400​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

15 terms of the series should be taken to get the sum of 14400.

Given,

A series 1³+2³+3³+.....

To Find,

How many terms of the series should be taken to get the sum of 14400.

Solution,

The formula for calculating the sum of series  1³+2³+3³+... is

[n(n+1)/2]²

where n is the number of terms

Now, according to the question

[n(n+1)/2]² = 14400

n(n+1)/2 = √14400 = 120

n²+n = 240

n²+n-240 = 0

On solving the quadratic equation, the value of n comes out to be 15 and -16.

The value -16 will be rejected as the number of terms cannot be negative.

Hence, 15 terms of the series should be taken to get the sum of 14400.

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