HARD
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The sum to infinity of the series,
1 + 2 1 - 1 n + 3 1 - 1 n 2 + ... is

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Important Questions on Sequences and Series

MEDIUM

If 2019+2212018+32122017+...+202119=k2019, then k is equal to _____.

HARD
Let S=2+67+1272+2073+3074+.. then 4S is equal to
MEDIUM
Let a1,a2,a3, be an A.P. If r=1ar2r=4, then 4a2 is equal to ______.
MEDIUM

For kN, if the sum of the series 1+4k+8k2+13k3+19k4+...... is 10, then the value of k is

MEDIUM
The sum of the infinite series 1+23+732+1233+1734+2235+ is equal to:
MEDIUM
Let S=109+1085+10752+.+25107+15108. Then the value of 16S-(25)-54 is equal to
MEDIUM
The sum 1+2·3+3·32+..+10·39 is equal to
EASY
Let a<1, b<1, c<1 and x=n=0an, y=n=0bn, z=n=0cn. If 1x, 1y and 1z are in Arithmetic Progression, then
MEDIUM
The sum of the series 1372.2.1+1973.3.2+2574.4.3+.... up to infinity is
MEDIUM

If the value of 1+23+632+1033+.. upto log0.2513+132+133+. upto  is l, then l2 is equal to             .

HARD
If ecos2x+cos4x+cos6x+....loge2 satisfies the equation t2-9t+8=0, then the value of 2sinxsinx+3cosx, where 0<x<π2, is equal to
EASY
If 112+122+132+ to =π26 then the value of 112+132+152+ to is
MEDIUM
Suppose a1,a2,2,a3,a4 be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is 492, then a4 is equal to ______________
MEDIUM
If α,β and γ are three consecutive terms of a non-constant G.P. Such that the equations αx2+2βx+γ=0 and x2+x-1=0 have a common root, then αβ+γ is equal to:
MEDIUM
The sum of infinite number of terms of a Geometric Progression is 3 and the sum of the squares of its terms is 92. The sum of the cubes of its terms is
MEDIUM
If S=75+952+1353+1954+, then 160 S is equal to                   .
HARD
The sum of the series 121·2+12+222·3+12+22+323·4+  upto 20 terms is
MEDIUM
If (10)9+2(11)1(10)8+3(11)2(10)7+......+10(11)9 =k(10)9, then k is equal to :
HARD
If the sum of n terms of the series 1+45+752+1053+ is l+15161-15n-1-(3n-2)4(5n-1), then l is