Sequences and Series
If sinβ is the geometric mean between sinα cosα then cos2β is equal to :
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The 8th and 14th term of a H.P. are 1/2 and 1/3, respectively. Find its 20th term. Also, find its general term.
If the sum to infinity of the series 3+(3+d)41+(3+2d)421+∞
, then find ¨
are in G.P. and a−b,c−a,andb−c
are in H.P., then prove that a+4b+c
is equal to 0.
are in A.P., then prove that the following are also in A.P.
Prove that b2c2+c2a2+a2+b2>abc×(a+b+c)(a,b,c>0)
are A.M.s between 2 and 12, then find the sum a+b+c+d+e+f˙
are in A.P., the find the value of a−4b+6c−4d+e˙
Find the sum of the series