MEDIUM
JEE Main/Advance
IMPORTANT
Earn 100

If G be the G.M. between a and b, show that 1G2-a2+1G2-b2=1ab=1G2.

Important Questions on Sequences and Series

EASY
JEE Main/Advance
IMPORTANT
Evaluate nth  term of the series : 24+442+643+844+
MEDIUM
JEE Main/Advance
IMPORTANT
Find the sum of the series : 23+43+63++183.
HARD
JEE Main/Advance
IMPORTANT
Find the sum of first n terms of the series whose nth  term is given by an=n3+3n2+2n .
MEDIUM
JEE Main/Advance
IMPORTANT
The fourth power of the common difference of an arithmetic progression with integer entries is added to the product of any four consecutive terms of it. Prove that resulting sum is the square of an integer.
HARD
JEE Main/Advance
IMPORTANT
Find a rational number, which when expressed as a decimal, will have 0.38¯  as its expansion.
MEDIUM
JEE Main/Advance
IMPORTANT
Find the sum of the series : 1-32+54-78+
MEDIUM
JEE Main/Advance
IMPORTANT
If for the sequence an,a2=3,a4=13 and a7=113, then find a1 if an=an2+bn+c,nN.
HARD
JEE Main/Advance
IMPORTANT

If a1,a2,a3,......,an be an A.P. of non-zero terms, then prove that:1a1a2+1a2a3+........+1an-1an=n-1a1an.