Sequences and Series

The value of k=1 (-1)k+1 ( k(k+1)k! ) is

1. e/2
2. e
3. 2/e
4. 1/e

The common difference of the A.P.: a1, a2, , am is 13 more than the common difference of the A.P.: b1, b2, , bn. If b31 = -277, b43 = -385 and a78 = 327, then a1 is equal to

1. 21
2. 19
3. 24
4. 16

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R - (a, b), then a2 + b2 is equal to .

6326 + 10 1325 + 10 2324 + 10 22323 + + 10 2243 is equal to :

1. 226
2. 325
3. 326
4. 225

If r=125 ( rr4 + r2 + 1 ) = pq, where p and q are positive integers such that (p, q) = 1, then p + q is equal to .

Let 729, 81, 9, 1, be a sequence and Pn denote the product of the first n terms of this sequence. If 2 n=140(Pn) 1n = 3 -13 and ( , ) = 1, then + is equal to

1. 73
2. 74
3. 75
4. 76

Consider an A.P.: a1, a2, , an; a1 > 0. If a2 - a1 = -34, an = 14a1, and i=1n ai = 5252, then i=117 ai is equal to

1. 238
2. 136
3. 476
4. 952

Let a1, a2, a3, a4 be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a1 + a2 + a3 + a4 = 48 and a1a2a3a4 + l4 = 361, then the largest term of the A.P. is equal to

1. 27
2. 24
3. 23
4. 21

( 13 + 47 ) + ( 132 + 13 47 + 4272 ) + ( 133 + 132 47 + 13 4272 + 4373 ) + up to infinite terms, is equal to

1. 74
2. 43
3. 65
4. 52

Let k=1n ak = n2 + n. If a10 = 59 and a6 = 7a1, then + is equal to :

1. 3
2. 5
3. 7
4. 12