Sequences and Series
The maximum sum of the series 20+1931+1832+⋯ is
Fill in the blanks in the following table, given that a is the first term, d the common difference and anthe nth term of the AP:
Find the sum to indicated number of terms in each of the geometric progressions : x3,x5,x7,n˙˙˙terms (ifx=±1).
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
If a, b, c, d and p are different real numbers such that (a2+b2+c2)p2−2(ab+bc+cd)p+(b2+c2+d2)≤0, then show that a, b, c and d are in G.P.