11th Maths Weekly Test - 4 ( Binomial Theorem, Sequences and Series )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 4 ( Binomial Theorem, Sequences and Series )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

Find 3 numbers in GP where sum is 24 and product is 216.

Sum the series: (1 + x) + (1 + x + x²) + (1 + x + x² +x³) + ... up to n terms

Expand \({1\over (3+2x)^2}\)in powers of x. Find a condition on x for which the expansion is valid.

Find all the sequence which are simultaneously arithmetic and geometric progression.

If p^th term of an AP is q and q^th term is p, find (p + q)^th term.

Show that \({ x }^{ n }=1+n\left( 1-\frac { 1 }{ x } \right) +\frac { n(n+1) }{ 1.2 } \left( 1-\frac { 1 }{ x } \right) ^{ 2 }+...\)

Write the first 6 terms of the sequences whose n^th terms are given below and classify them as arithmetic progression, geometric progression, arithmetic-geometric progression, harmonic progression and none of them. \(\frac { 1 }{ 2^{ n+1 } } \)

Write the first 6 terms of the sequences whose n^th terms are given below and classify them as arithmetic progression, geometric progression, arithmetic geometric progression, harmonic progression and none of them \(\frac { \left( n+1 \right) \left( n+2 \right) }{ \left( n+3 \right) (n+4) } \)

Write the first 4 terms of the logarithmic series of \(\log { \left( \frac { 1+3x }{ 1-3x } \right) } \)

If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x+ y)ⁿ are equal.

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11th Maths Weekly Test - 4 ( Binomial Theorem, Sequences and Series )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 4 ( Binomial Theorem, Sequences and Series )-Aug 2020

Part - A

Generic 3 - Answer All Question

Find 3 numbers in GP where sum is 24 and product is 216.

Sum the series: (1 + x) + (1 + x + x2) + (1 + x + x2 +x3) + ... up to n terms

Expand \({1\over (3+2x)^2}\)in powers of x. Find a condition on x for which the expansion is valid.

Find all the sequence which are simultaneously arithmetic and geometric progression.

If pth term of an AP is q and qth term is p, find (p + q)th term.

Show that \({ x }^{ n }=1+n\left( 1-\frac { 1 }{ x } \right) +\frac { n(n+1) }{ 1.2 } \left( 1-\frac { 1 }{ x } \right) ^{ 2 }+...\)

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic-geometric progression, harmonic progression and none of them. \(\frac { 1 }{ 2^{ n+1 } } \)

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic geometric progression, harmonic progression and none of them \(\frac { \left( n+1 \right) \left( n+2 \right) }{ \left( n+3 \right) (n+4) } \)

Write the first 4 terms of the logarithmic series of \(\log { \left( \frac { 1+3x }{ 1-3x } \right) } \)

If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x+ y)n are equal.

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Sum the series: (1 + x) + (1 + x + x²) + (1 + x + x² +x³) + ... up to n terms

If p^th term of an AP is q and q^th term is p, find (p + q)^th term.

Write the first 6 terms of the sequences whose n^th terms are given below and classify them as arithmetic progression, geometric progression, arithmetic-geometric progression, harmonic progression and none of them. \(\frac { 1 }{ 2^{ n+1 } } \)

Write the first 6 terms of the sequences whose n^th terms are given below and classify them as arithmetic progression, geometric progression, arithmetic geometric progression, harmonic progression and none of them \(\frac { \left( n+1 \right) \left( n+2 \right) }{ \left( n+3 \right) (n+4) } \)

If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x+ y)ⁿ are equal.