Sequences and Series
If sinx+cosx=y+y1,xϵ[0,π] and y>0, then-
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Write the first five terms of the sequence whose nthterms are : an=n(n+2)
In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is 112.
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
If a−bxa+bx=b−cxb+cx=c−dxc+dx(x=0),then show that a, b, c and d are in G.P.
Find the sum of the following series up to n terms:(i) 5+55+555+.... (ii) .6+.66+.666+....
How many terms of the A.P. 6, −211,−5,˙˙˙are needed to give the sum 25?
How many terms of the AP: 9, 17, 25, . . . must be taken to give a sum of 636?