C1-2 C2-3 C3-4 C4-n Cn-A- 2xB- n - 2nC- n - 2x-1D- n - 2n-1

The correct option is C Trick : nbsp;Put n = 1, 2, 3,....... S_1 = 1, S_2 = 2 + 2 = 4 Now by alternate (c), put n = 1,2 S_1 = 1.2^0 = 1, S_2 = 2.2^1 = 4 ...

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Standard XII

Mathematics

Logarithms

C1+2 C2+3 C3+...

Question

$C_{1} + 2 C_{2} + 3 C_{3} + 4 C_{4} + . . . . . . + n C_{n}$ =

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Solution

The correct option is C

Trick : Put n = 1, 2, 3,.......

$S_{1} = 1, S_{2} = 2 + 2 = 4$

Now by alternate (c), put n = 1,2

$S_{1} = {1.2}^{0} = 1, S_{2} = {2.2}^{1} = 4$

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Similar questions

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C1+2C2+3C3+4C4+......+nCn =

The correct option is C Trick : Put n = 1, 2, 3,....... S1=1,S2=2+2=4 Now by alternate (c), put n = 1,2 S1=1.20=1,S2=2.21=4

$C_{1} + 2 C_{2} + 3 C_{3} + 4 C_{4} + . . . . . . + n C_{n}$ =

The correct option is C

Trick : Put n = 1, 2, 3,.......

$S_{1} = 1, S_{2} = 2 + 2 = 4$

Now by alternate (c), put n = 1,2

$S_{1} = {1.2}^{0} = 1, S_{2} = {2.2}^{1} = 4$