Show that: C 0 - C 1 (1+x / 1+nx) + C 2 [1+2x / (1+nx) 2 ] - C 3 [1+3x / (1+nx) 3 ] + ……..= 0 Find the sum of the series: ∑ (-1) r . n C r (1/2 r + 3 r /2 2r + 7 r /2 3r + …… + up to m terms ) r goes from 0 to n.

Question

Show that: C 0 - C 1 (1+x / 1+nx) + C 2 [1+2x / (1+nx) 2 ] - C 3 [1+3x / (1+nx) 3 ] + &hellip;&hellip;..= 0 Find the sum of the series: &sum; (-1) r . n C r (1/2 r + 3 r /2 2r + 7 r /2 3r + &hellip;&hellip; + up to m terms ) r goes from 0 to n.

Askiitians Academic Expert · Answer

Dear Prathamesh, In order to get the sum of the series you have to provide the first three terms , then only one can understand what is the nature of the series. For e.g, if I give a series as follows, 2 , 4 , .......................................................... till n th term Now can you tell me is it in G.P or A.P or A.G.P or H.P Ofcourse not! So this is the problem in the question: 8/5 + 16/65 + ..................................+ 128/2 18 + 1 .

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Show that: C 0 - C 1 (1+x / 1+nx) + C 2 [1+2x / (1+nx) 2 ] - C 3 [1+3x / (1+nx) 3 ] + ……..= 0 Find the sum of the series: ∑ (-1) r . n C r (1/2 r + 3 r /2 2r + 7 r /2 3r + …… + up to m terms ) r goes from 0 to n.

Show that:           C₀- C₁(1+x / 1+nx) + C₂[1+2x / (1+nx) ²] - C₃[1+3x / (1+nx)³] + ……..= 0



Find the sum of the series: ∑ (-1) ^r. ⁿC_r (1/2^r + 3^r/2^2r + 7^r/2^3r + …… + up to m terms)       r goes from 0 to n.

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Show that: C 0 - C 1 (1+x / 1+nx) + C 2 [1+2x / (1+nx) 2 ] - C 3 [1+3x / (1+nx) 3 ] + ……..= 0 Find the sum of the series: ∑ (-1) r . n C r (1/2 r + 3 r /2 2r + 7 r /2 3r + …… + up to m terms ) r goes from 0 to n.

Show that: C0 - C1 (1+x / 1+nx) + C2 [1+2x / (1+nx) 2] - C3 [1+3x / (1+nx) 3] + ……..= 0 Find the sum of the series: ∑ (-1) r. nCr (1/2r + 3r/22r + 7r/23r + …… + up to m terms) r goes from 0 to n.

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Show that: C₀- C₁(1+x / 1+nx) + C₂[1+2x / (1+nx) ²] - C₃[1+3x / (1+nx)³] + ……..= 0

Find the sum of the series: ∑ (-1) ^r. ⁿC_r (1/2^r + 3^r/2^2r + 7^r/2^3r + …… + up to m terms) r goes from 0 to n.