共50条信息
\((\)Ⅱ\()\)设\(b_{n}=\dfrac{n}{{a}_{n}+1} \),求数列\(\{b_{n}\}\)的前\(n\)项和\(S_{n}\);
\((\)Ⅲ\()\)在条件\((\)Ⅱ\()\)下对任意正整数\(n\),不等式\(S_{n}+\dfrac{n+1}{{2}^{n}} -1 > (-1)^{n}⋅a\)恒成立,求实数\(a\)的取值范围\(.\)
已知等比数列\(\left\{{a}_{n}\right\} \)单调递增,记数列\(\left\{{a}_{n}\right\} \)的前\(n \)项之和为\({S}_{n} \),且满足条件\({a}_{2}=6,{S}_{3}=26 \)
\((\)Ⅰ\()\)求数列\(\left\{{a}_{n}\right\} \)的通项公式;
\((\)Ⅱ\()\)设\({b}_{n}={a}_{n}-2n \),求数列\(\left\{{b}_{n}\right\} \)的前\(n \)项之和\({T}_{n} \).
已知函数\(f\left(x\right)= \dfrac{2}{3}x \),数列\(\left\{{a}_{n}\right\} \)中\({a}_{n} > 0 \),满足\({a}_{n+1}=f\left({a}_{n}\right) (n\in {{N}^{*}})\),且\({{a}_{5}}\cdot {{a}_{8}}=\dfrac{8}{27}\)
\((1)\)求数列\(\left\{{a}_{n}\right\} \)的通项;
\((2)\)若数列\(\left\{{b}_{n}\right\} \)的前\(n\)项和为\({S}_{n} \),且\({b}_{n}={a}_{n}+n \),求\({S}_{n} \)
已知数列\(\left\{{a}_{n}\right\} \)满足\({a}_{1}=1,n{a}_{n+1}=2(n+1){a}_{n} \)设\({b}_{n}= \dfrac{{a}_{n}}{n} \)
\((1)\)求\({b}_{1},{b}_{2},{b}_{3} \);
\((2)\)判断数列\(\left\{{b}_{n}\right\} \)是否为等比数列,并说明理由。
\((3)\)求\(\left\{{a}_{n}\right\} \)的通项公式。
已知等差数列\(\left\{ {{a}_{n}} \right\}\),\({{S}_{n}}\)为其前\(n\)项和,\({{a}_{5}}=10,{{S}_{7}}=56.\)
\((I)\)求数列\(\left\{ {{a}_{n}} \right\}\)的通项公式; \((II)\)若\({{b}_{n}}={{a}_{n}}+{{(\sqrt{3})}^{{{a}_{n}}}}\),求数列\(\left\{ {{b}_{n}} \right\}\)的前\(n\)项和\({{T}_{n}}\).
设等比数列\(\{a_{n}\}\)的公比为\(q\),则“\(0 < q < 1\)”是“\(\{a_{n}\}\)是递减数列”的
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