Discussion

Explanation:

Given: (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280

⇒ (2n + 2n +.... + 2n) + (1 +3 + 5 +.... + 47) = 5280

Odd numbers from 1 to 47 are added in the above series.

n^th odd natural number = 2n - 1

∴ Number of terms from 1 to 47 = (47 + 1)/2 = 24 terms

∴ Given equation becomes 2n × 24 + (1 + 3 + 5 + … + 47) = 5280

Sum of first n odd natural numbers = n².

⇒ 2n × 24 + 24² = 5280

⇒ 2n × 24 = 5280 - 24²

⇒ 2n = 220 - 24

⇒ n = 98

Hence, 1 + 2 + 3 + ... + 98 = $\frac{98\times 99}{2}$ = 4851.

Hence, 4851.

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