# JEE Main & Advanced Mathematics Other Series Question Bank

### done nth term of special series, Sum to n terms and Infinite number of terms

• A) $\frac{n}{n+1}$

B) $\frac{2n}{n+1}$

C) $\frac{2}{n\,(n+1)}$

D) $\frac{2\,(n+1)}{n+2}$

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• A) $\frac{n\,(n+1)\,(2n+1)}{6}$

B) $\frac{{{n}^{2}}(n+1)}{4}$

C) $\frac{n\,(n-1)\,(2n-1)}{6}$

D) ${{n}^{2}}$

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• A) $\frac{n{{(n+1)}^{2}}}{2}$

B) $\frac{1}{2}{{n}^{2}}(n+1)$

C) $n{{(n+1)}^{2}}$

D) None of these

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• A) $\frac{n(n+1)(2n+1)}{3}$

B) $\frac{2n(n+1)(2n+1)}{3}$

C) $\frac{n(n+1)(2n+1)}{6}$

D) $\frac{n(n+1)(2n+1)}{9}$

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• A) ${{n}^{2}}-2n+6$

B) $\frac{n(n+1)(2n-1)}{6}$

C) ${{n}^{2}}+2n+6$

D) $\frac{n(n+1)(n+2)}{6}$

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• A) $\frac{n(n+1)(n+2)}{3}$

B) $\frac{(n+1)(n+2)(n+3)}{12}$

C) ${{n}^{2}}(n+2)$

D) $n(n+1)(n+2)$

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• A) $3\,(n\,!)\,+\,n-3$

B) $(n+1)!\,-\,(n-1)!$

C) $(n+1)\,!\,-1$

D) $2\,(n\,!)-2n-1$

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• A) $\frac{1}{n(n+1)}$

B) $\frac{n}{n+1}$

C) $\frac{2n}{n+1}$

D) $\frac{2}{n(n+1)}$

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• A) ${{n}^{3}}+{{n}^{2}}+n+2$

B) $\frac{1}{6}(2{{n}^{3}}+12{{n}^{2}}+10n-84)$

C) ${{n}^{3}}+{{n}^{2}}+n$

D) None of these

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• A) $\frac{n(3n-1)}{2}$

B) $\frac{n(3n+1)}{2}$

C) $n(3n+2)$

D) $\frac{n(3n+1)}{4}$

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• A) $\frac{{{n}^{3}}{{(n+1)}^{3}}(2n+1)}{24}$

B) $\frac{n(n+1)(3{{n}^{2}}+7n+2)}{12}$

C) $\frac{n(n+1)}{6}[n(n+1)+(2n+1)]$

D) $\frac{n(n+1)}{12}[6n(n+1)+2(2n+1)]$

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• A) $n(n+1)(n+2)$

B) $(n+1)(n+2)(n+3)$

C) $\frac{1}{4}n(n+1)(n+2)(n+3)$

D) $\frac{1}{4}(n+1)(n+2)(n+3)$

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• A) 22000

B) 10,000

C) 14,400

D) 15,000

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• A) 8

B) 10

C) 15

D) 20

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• A) ${{\tan }^{-1}}\left( \frac{n}{n+2} \right)$

B) ${{\cot }^{-1}}\left( \frac{n+2}{n} \right)$

C) ${{\tan }^{-1}}(n+1)-{{\tan }^{-1}}1$

D) All of these

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• A) $\frac{n}{2}({{n}^{2}}-1)$

B) $\frac{n}{2}({{n}^{2}}+1)$

C) $\frac{2}{n}({{n}^{2}}+1)$

D) $\frac{2}{n}({{n}^{2}}-1)$

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• A) $\frac{n+1}{2}$

B) $\frac{n-1}{2}$

C) $\frac{{{n}^{2}}+1}{2}$

D) $\frac{{{n}^{2}}-1}{2}$

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• A) $\frac{1}{24}n(n-1)(n+1)(3n+2)$

B) $\frac{{{n}^{2}}}{48}(n-1)(n-2)$

C) $\frac{1}{6}n(n+1)(n+2)(n+5)$

D) None of these

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• A) 188090

B) 189080

C) 199080

D) None of these

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• A) $\frac{234}{25}$

B) $\frac{243}{35}$

C) $\frac{263}{27}$

D) None of these

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• A) $\frac{2n}{n+1}$

B) $\frac{4n}{n+1}$

C) $\frac{6n}{n+1}$

D) $\frac{9n}{n+1}$

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• A) $\frac{n\,(n+1)(9{{n}^{2}}+23n+13)}{6}$

B) $\frac{n\,(n-1)(9{{n}^{2}}+23n+12)}{6}$

C) $\frac{(n+1)(9{{n}^{2}}+23n+13)}{6}$

D) $\frac{n\,(9{{n}^{2}}+23n+13)}{6}$

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• A) $n-\frac{1}{2}({{3}^{n}}-1)$

B) $n+\frac{1}{2}({{3}^{n}}-1)$

C) $n+\frac{1}{2}(1-{{3}^{-n}})$

D) $n+\frac{1}{2}({{3}^{-n}}-1)$

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• A) $\frac{m(m+1)}{2}$

B) $\frac{m(m+1)(2m+1)}{6}$

C) $\frac{n(n+1)(2n+1)}{6}$

D) $\frac{n(n+1)}{2}$

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• A) ${{n}^{3}}$

B) $\frac{1}{3}n\,(n+1)(n+2)$

C) $\frac{1}{6}n\,(n+1)(n+2)$

D) $\frac{1}{3}n\,(n+1)(2n+1)$

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• A) Is divisible by 5

B) Is an odd integer divisible by 5

C) Is an even integer which is not divisible by 5

D) Is an odd integer which is not divisible by 5

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• A) $\frac{n}{6}(n+1)(6{{n}^{2}}+14n+7)$

B) $\frac{n}{6}(n+1)(2n+1)(3n+1)$

C) $4{{n}^{3}}+4{{n}^{2}}+n$

D) None of these

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• A) $\frac{{{n}^{2}}+n}{3}$

B) $\frac{{{n}^{3}}+8n}{3}$

C) $\frac{{{n}^{2}}+8n}{5}$

D) $\frac{{{n}^{2}}-8n}{3}$

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• A) $(n+1)\,(n+2)\,(n+3)/6$

B) $n\,(n+1)\,(n+2)/6$

C) $n\,(n+1)\,(2n+3)\,$

D) $n\,(n+1)\,(2n+1)/6$

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• A) 89

B) 97

C) 101

D) 123

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• A) 2481

B) 2483

C) 2485

D) 2487

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• A) $\infty$

B) 1

C) 0

D) None of these

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• A) ${{\left( \frac{n}{n+1} \right)}^{2}}$

B) ${{\left( \frac{n}{n+1} \right)}^{3}}$

C) $\left( \frac{n}{n+1} \right)$

D) $\left( \frac{1}{n+1} \right)$

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• A) $\frac{n(n+3)}{4}$

B) $\frac{n(n+2)}{4}$

C) $\frac{n(n+1)\,(n+2)}{6}$

D) ${{n}^{2}}$

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• A) $\frac{n\,(3n-1)}{2(n)\,!}$

B) $\frac{n\,(3n+1)}{2\,(n)\,!}$

C) $\frac{n}{2}\frac{3n}{(n)\,!}$

D) None of these

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• A) $\frac{4006}{3006}$

B) $\frac{4003}{3007}$

C) $\frac{4006}{3008}$

D) $\frac{4006}{3009}$

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• A) $\frac{{{\pi }^{4}}}{96}$

B) $\frac{{{\pi }^{4}}}{45}$

C) $\frac{89}{90}{{\pi }^{4}}$

D) None of these

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• A) $\frac{1}{1+a}$

B) $\frac{2}{1+a}$

C) $\infty$

D) None of these

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