Sequences and Series
Let b1>1 for i=1,2,……,101. Suppose logeb1,logeb10 are in Arithmetic progression (A.P.) with the common difference loge2. suppose a1,a2……….a101 are in A.P. such a1=b1anda51=b51. If t=b1+b2+……+b51ands=a1+a2+……+a51 then
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Number of real solutions of the equation sinaxcosax=4ax+a−x is
There are n Arithmetic means between 13 and 61. If ratio of the first A.M. and (n−1) the A.M. may be 16:55, then find n.
The sum of n arithmetic means between a and b, is
If A=cos2x+cos2x1,B=cosx−cosx1 ∀x=(2n±1)2π, then the minimum value of BA is
If a,b,c are sides of the △ABC such that (1+ab−c)a⋅(1+bc−a)b⋅(1+ca−b)c≥1, then triangle △ABC must be
Let A1 denotes arithmetic mean of two numbers a=1b=2. A2 denotes arithmetic mean of A1 and b. For n≥3,let An is arithmetic mean of An−1 and b , then
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Insert 19 arithmetic means between 41 and −943.