If ∑k=119(−2)kk!(19−k)!=−λ19! then λ equals.............

∑K=119(−2)k19!19!k!(19−k)! =119!∑K=119(−2)k. 19Ck =119![(1−2)19−1]=−219!

If ∑k=119(−2)kk!(19−k)!=−λ19! then λ equals.............

∑K=119(−2)k19!19!k!(19−k)! =119!∑K=119(−2)k. 19Ck =119![(1−2)19−1]=−219!

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If $\sum_{k = 1}^{19} \frac{{(- 2)}^{k}}{k! (19 - k)!} = \frac{- λ}{19!}$ then $λ$ equals.............

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$\begin{array}{l} \sum_{K = 1}^{19} \frac{{(- 2)}^{k} 19!}{19! k! (19 - k)!} = \frac{1}{19!} \sum_{K = 1}^{19} {(- 2)}^{k} .^{19} C_{k}^{} \end{array} = \frac{1}{19!} [{(1 - 2)}^{19} - 1] = \frac{- 2}{19!}$

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If ∑k=119(−2)kk!(19−k)!=−λ19! then λ equals.............

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If $\sum_{k = 1}^{19} \frac{{(- 2)}^{k}}{k! (19 - k)!} = \frac{- λ}{19!}$ then $λ$ equals.............