Class 11

Math

Algebra

Sequences and Series

The value of p if ,the mean of $23,25,p$ is 24

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If $a,b,>0$ such that $a_{3}+b_{3}=2,$ then show that $a+b≤2.$

Find the sum of the series $3_{2}+11 +4_{2}+21 +5_{2}+31 +6_{2}+41 +∞$

If $a,b,c$ are in A.P., then prove that the following are also in A.P. $a_{2}(b+c),b_{2}(c+a),c_{2}(a+b)$

Prove that a sequence in an A.P., if the sum of its $n$ terms is of the form $An_{2}+Bn,whereA,B$ are constants.

Find the sum to $n$ terms of the series $3/(1_{2}×2_{2})+5/(2_{2}×3_{2})+7/(3_{2}×4_{2})+˙$

If $x,1,andz$ are in A.P. and $x,2,andz$ are in G.P., then prove that $x,and4,z$ are in H.P.

Find the term of the series $25,2243 ,2021 ,1841 $ which is numerically the smallest.

Find the least value of $secA+secB+secC$ in an acute angled triangle.