Class 11MathematicsSequences and Seriesnth term of special series, Sum to n terms and Infinite number of terms
EasyLet $a_n = (1^2 + 2^2 + \ldots + n^2)^n$ and $b_n = n^n(n!)$. Then
- A$a_n < b_n$ for all $n$
- B$a_n > b_n$ for all $n$
- C$a_n = b_n$ for infinitely many $n$
- D$a_n < b_n$ if $n$ is even and $a_n > b_n$ if $n$ is odd
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Find the sum to $n$ terms of the series whose $n^{th}$ term is given by $a_n = n^2 + 2^n$.
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View SolutionFind the sum of the following series up to $n$ terms:
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$\frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\ldots$
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View SolutionFind the sum of the following series up to $n$ terms:
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$0.6 + 0.66 + 0.666 + \dots$
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