Class 11

Math

Algebra

Sequences and Series

If $A=cos_{2}x+cos_{2}x1 ,B=cosx−cosx1 ∀x=(2n±1)2π $, then the minimum value of $BA $ is

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If $a,b,c,d,e,f$ are A.M.s between 2 and 12, then find the sum $a+b+c+d+e+f˙$

If first three terms of the sequence $1/16,a,b,61 $ are in geometric series and last three terms are in harmonic series, then find the values of $aandb˙$

If $a,b,c$ are positive, then prove that $a/(b+c)+b/(c+a)+c/(a+b)≥3/2.$

Divide 32 into four parts which are in A.P. such that the ratio of the product of extremes to the product of means is 7:15.

Find the sum $21_{2} −2_{2}3_{2} +2_{3}5_{2} −2_{4}7_{2} +∞˙$

Prove that $[n+1/2]_{n}>(n!)˙$

If $a,b,c,d$ are in G.P., then prove that $(a_{3}+b_{3})_{−1},(b_{3}+c_{3})_{−1},(c_{3}+d_{3})_{−1}$ are also in G.P.

Find the sum of the series $1×22 +2×35 ×2+3×410 ×2_{2}+4×517 ×2_{3}+→n$ terms.