Q.6. The sum upto 10 terms is equal to :

Q: What is the correct answer for JEE Main Mathematics Q6?

The correct answer is C. Sol. The $n$-th term of the series is $T_n = \frac{1^2+2^2+\dots+n^2}{n} = \frac{n(n+1)(2n+1)}{6n} = \frac{(n+1)(2n+1)}{6}$. We need to find the sum of the first 10 terms, $S_{10} = \sum_{n=1}^{10} T_n = \sum_{n=1}^{10} \frac{(n+1)(2n+1)}{6} = \frac{1}{6} \sum_{n=1}^{10} (2n^2 + 3n + 1)$. $S_{10} = \frac{1}{6} \left( 2\sum_{n=1}^{10} n^2 + 3\sum_{n=1}^{10} n + \sum_{n=1}^{10} 1 \right)$. Using sum

Q: Q.6. The sum upto 10 terms is equal to :

The correct answer is C. Sol. The $n$-th term of the series is $T_n = \frac{1^2+2^2+\dots+n^2}{n} = \frac{n(n+1)(2n+1)}{6n} = \frac{(n+1)(2n+1)}{6}$. We need to find the sum of the first 10 terms, $S_{10} = \sum_{n=1}^{10} T_n = \sum_{n=1}^{10} \frac{(n+1)(2n+1)}{6} = \frac{1}{6} \sum_{n=1}^{10} (2n^2 + 3n + 1)$. $S_{10} = \frac{1}{6} \left( 2\sum_{n=1}^{10} n^2 + 3\sum_{n=1}^{10} n + \sum_{n=1}^{10} 1 \right)$. Using sum

Q: What are the options for this JEE Main Mathematics question?

A. 130 · B. 155 · C. $\frac{315}{2}$ · D. $\frac{325}{2}$

Question

Q.6. The sum  upto 10 terms is equal to :

FirstInTest · Accepted Answer

Sol. The $n$-th term of the series is $T_n = \frac{1^2+2^2+\dots+n^2}{n} = \frac{n(n+1)(2n+1)}{6n} = \frac{(n+1)(2n+1)}{6}$. We need to find the sum of the first 10 terms, $S_{10} = \sum_{n=1}^{10} T_n = \sum_{n=1}^{10} \frac{(n+1)(2n+1)}{6} = \frac{1}{6} \sum_{n=1}^{10} (2n^2 + 3n + 1)$. $S_{10} = \frac{1}{6} \left( 2\sum_{n=1}^{10} n^2 + 3\sum_{n=1}^{10} n + \sum_{n=1}^{10} 1 \right)$. Using sum formulas: $\sum n = \frac{n(n+1)}{2}$ and $\sum n^2 = \frac{n(n+1)(2n+1)}{6}$. $S_{10} = \frac{1}{6} \left( 2\frac{10(10+1)(2\cdot10+1)}{6} + 3\frac{10(10+1)}{2} + 10 \right)$. $S_{10} = \frac{1}{6} \left( 2\frac{10 \cdot 11 \cdot 21}{6} + 3\frac{10 \cdot 11}{2} + 10 \right)$. $S_{10} = \frac{1}{6} \left( 2 \cdot 5 \cdot 11 \cdot 7 + 3 \cdot 5 \cdot 11 + 10 \right)$. $S_{10} = \frac{1}{6} \left( 770 + 165 + 10 \right) = \frac{1}{6} (945) = \frac{315}{2}$.

Answer

130

Answer

155

Answer

$\frac{315}{2}$

Answer

$\frac{325}{2}$

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