Question
Download Solution PDFSuppose the nth term of a series is \(1+\frac{n}{2}+\frac{n^{2}}{2} \). If there are 20 terms in the series, then the sum of the series is equal to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
nth term = 1 + n/2 + n2/2
Sum of natural numbers = n(n+1)/2
Sum of square of 'n' natural numbers = [n(n+1)(2n+1)]/6
Calculation:
For understanding, breaking the terms given in question as :
1. Adding one twenty times = 20
2. When n = 1, 2, 3 and so on up to 20 in n/2, the sum = 1/2 (n(n+1)/2)
= 1/2 (20(20+1)/2) = 105
3. When n = 1, 2, 3 and so on up to 20 in n2/2, the sum = 1/2 [n(n+1)(2n+1)]/6
= 1/2 [20(20+1)(2×20+1)]/6 = 1435
Therefore, sum of the series = 20 + 105 + 1435 = 1560
Hence, option 4 is correct.
Last updated on Apr 2, 2025
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